This document provides an overview of a thesis that systematically compares two functional methods - Dyson-Schwinger equations (DSE) and the functional renormalization group (FRG) - in low-energy quantum chromodynamics (QCD) models. It motivates the research by explaining that non-perturbative approaches are needed to understand many features of QCD. It then provides basics on the two functional methods and shows results from applying the FRG to quark meson models, including approximations. Finally, it outlines a plan to formally and practically compare the DSE and FRG methods by applying them to specific low-energy QCD models and analyzing their intrinsic properties and numerical results.
The document summarizes several advanced policy gradient methods for reinforcement learning, including trust region policy optimization (TRPO), proximal policy optimization (PPO), and using the natural policy gradient with the Kronecker-factored approximation (K-FAC). TRPO frames policy optimization as solving a constrained optimization problem to limit policy updates, while PPO uses a clipped objective function as a pessimistic bound. Both methods improve upon vanilla policy gradients. K-FAC provides an efficient way to approximate the natural policy gradient using the Fisher information matrix. The document reviews the theory and algorithms behind these methods.
In this work, we propose to apply trust region optimization to deep reinforcement
learning using a recently proposed Kronecker-factored approximation to
the curvature. We extend the framework of natural policy gradient and propose
to optimize both the actor and the critic using Kronecker-factored approximate
curvature (K-FAC) with trust region; hence we call our method Actor Critic using
Kronecker-Factored Trust Region (ACKTR). To the best of our knowledge, this
is the first scalable trust region natural gradient method for actor-critic methods.
It is also a method that learns non-trivial tasks in continuous control as well as
discrete control policies directly from raw pixel inputs. We tested our approach
across discrete domains in Atari games as well as continuous domains in the MuJoCo
environment. With the proposed methods, we are able to achieve higher
rewards and a 2- to 3-fold improvement in sample efficiency on average, compared
to previous state-of-the-art on-policy actor-critic methods. Code is available at
https://github.com/openai/baselines.
Minimum uncertainty coherent states attached to nondegenerate parametric ampl...Sergio Floquet
The document summarizes research on minimum uncertainty coherent states for a nondegenerate parametric amplifier. It begins by introducing the Hamiltonian for a nondegenerate parametric amplifier and shows its equivalence to a two-dimensional harmonic oscillator Hamiltonian through a similarity transformation. It then discusses how the eigenstates of the two-dimensional harmonic oscillator Hamiltonian can be used to obtain new eigenstates for the parametric amplifier Hamiltonian. These new eigenstates are called displaced SU(2)-Perelomov coherent states and satisfy the eigenvalue equation for the parametric amplifier Hamiltonian. They form a complete set of eigenbasis vectors with the property of minimum uncertainty.
Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...Stephan Irle
This presentation was given April 27, 2013 at Ibaraki University in Mito, Japan (Professor Seiji Mori's group). The presentation does not claim to give a complete overview of the complex field of DFTB parameterization, but rather focuses on the method's central approximations and discusses its performance in various applications.
Recent developments for the quantum chemical investigation of molecular syste...Stephan Irle
The structural complexity of molecular clusters increases with size due to the associated, rapidly growing configuration space. Two examples are realized in i) the transition from molecular to bulk systems, and ii) in the subsequent chemical functionalization of nanomaterials. In such systems, traditional quantum chemical approaches of investigations are hampered by the vastly increasing computational cost, even considering ever-growing supercomputer capabilities. Computationally inexpensive, yet accurate schemes such as the density-functional tight-binding (DFTB) method promise here a significant advantage.
We have recently engaged in developing novel methodologies for systems with increasing structural complexity, driven by motivation from experimental studies. In this presentation, we will briefly review a) our advances in the automatic parameterization of DFTB, and b) the Kick-fragment-based “CrazyLego” conformationally aware approach for studying molecular and ionic liquid clusters with increasing size.
What can we learn from molecular dynamics simulations of carbon nanotube and ...Stephan Irle
The document summarizes molecular dynamics simulations of carbon nanotube and graphene growth performed by the author and collaborators. It describes how density functional tight-binding molecular dynamics simulations were used to study: [1] acetylene decomposition on iron clusters, which led to polyacetylene formation and carbon cluster attachment; [2] cap nucleation by supplying carbon atoms to an iron cluster and annealing; and [3] sidewall growth through carbon atom insertion and ring formation. The simulations provided insights into carbon nanotube growth mechanisms at an atomic scale that are difficult to observe experimentally.
This document presents a new algorithm for flexible route planning that allows customizing a linear combination of two metrics like travel time and cost. The algorithm precomputes shortcuts for a graph based on contracting nodes in a customized order. It develops the concept of "gradual parameter interval splitting" to improve the node ordering for different parameter values. The algorithm combines node contraction with a goal-directed technique to further improve performance of flexible queries.
An Effectively Modified Firefly Algorithm for Economic Load Dispatch ProblemTELKOMNIKA JOURNAL
This paper proposes an effectively modified firefly algorithm (EMFA) for searching optimal solution of economic load dispatch (ELD) problem. The proposed method is developed by improving the procedure of new solution generation of conventional firefly algorithm (FA). The performance of EMFA is compared to FA variants and other existing methods by testing on four different systems with different types of objective function and constraints. The comparison indicates that the proposed method can reach better optimal solutions than other FA variants and most other existing methods with lower population and lower maximum iteration. As a result, it can lead to a conclusion that the proposed method is potential for ELD problem.
The document summarizes several advanced policy gradient methods for reinforcement learning, including trust region policy optimization (TRPO), proximal policy optimization (PPO), and using the natural policy gradient with the Kronecker-factored approximation (K-FAC). TRPO frames policy optimization as solving a constrained optimization problem to limit policy updates, while PPO uses a clipped objective function as a pessimistic bound. Both methods improve upon vanilla policy gradients. K-FAC provides an efficient way to approximate the natural policy gradient using the Fisher information matrix. The document reviews the theory and algorithms behind these methods.
In this work, we propose to apply trust region optimization to deep reinforcement
learning using a recently proposed Kronecker-factored approximation to
the curvature. We extend the framework of natural policy gradient and propose
to optimize both the actor and the critic using Kronecker-factored approximate
curvature (K-FAC) with trust region; hence we call our method Actor Critic using
Kronecker-Factored Trust Region (ACKTR). To the best of our knowledge, this
is the first scalable trust region natural gradient method for actor-critic methods.
It is also a method that learns non-trivial tasks in continuous control as well as
discrete control policies directly from raw pixel inputs. We tested our approach
across discrete domains in Atari games as well as continuous domains in the MuJoCo
environment. With the proposed methods, we are able to achieve higher
rewards and a 2- to 3-fold improvement in sample efficiency on average, compared
to previous state-of-the-art on-policy actor-critic methods. Code is available at
https://github.com/openai/baselines.
Minimum uncertainty coherent states attached to nondegenerate parametric ampl...Sergio Floquet
The document summarizes research on minimum uncertainty coherent states for a nondegenerate parametric amplifier. It begins by introducing the Hamiltonian for a nondegenerate parametric amplifier and shows its equivalence to a two-dimensional harmonic oscillator Hamiltonian through a similarity transformation. It then discusses how the eigenstates of the two-dimensional harmonic oscillator Hamiltonian can be used to obtain new eigenstates for the parametric amplifier Hamiltonian. These new eigenstates are called displaced SU(2)-Perelomov coherent states and satisfy the eigenvalue equation for the parametric amplifier Hamiltonian. They form a complete set of eigenbasis vectors with the property of minimum uncertainty.
Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...Stephan Irle
This presentation was given April 27, 2013 at Ibaraki University in Mito, Japan (Professor Seiji Mori's group). The presentation does not claim to give a complete overview of the complex field of DFTB parameterization, but rather focuses on the method's central approximations and discusses its performance in various applications.
Recent developments for the quantum chemical investigation of molecular syste...Stephan Irle
The structural complexity of molecular clusters increases with size due to the associated, rapidly growing configuration space. Two examples are realized in i) the transition from molecular to bulk systems, and ii) in the subsequent chemical functionalization of nanomaterials. In such systems, traditional quantum chemical approaches of investigations are hampered by the vastly increasing computational cost, even considering ever-growing supercomputer capabilities. Computationally inexpensive, yet accurate schemes such as the density-functional tight-binding (DFTB) method promise here a significant advantage.
We have recently engaged in developing novel methodologies for systems with increasing structural complexity, driven by motivation from experimental studies. In this presentation, we will briefly review a) our advances in the automatic parameterization of DFTB, and b) the Kick-fragment-based “CrazyLego” conformationally aware approach for studying molecular and ionic liquid clusters with increasing size.
What can we learn from molecular dynamics simulations of carbon nanotube and ...Stephan Irle
The document summarizes molecular dynamics simulations of carbon nanotube and graphene growth performed by the author and collaborators. It describes how density functional tight-binding molecular dynamics simulations were used to study: [1] acetylene decomposition on iron clusters, which led to polyacetylene formation and carbon cluster attachment; [2] cap nucleation by supplying carbon atoms to an iron cluster and annealing; and [3] sidewall growth through carbon atom insertion and ring formation. The simulations provided insights into carbon nanotube growth mechanisms at an atomic scale that are difficult to observe experimentally.
This document presents a new algorithm for flexible route planning that allows customizing a linear combination of two metrics like travel time and cost. The algorithm precomputes shortcuts for a graph based on contracting nodes in a customized order. It develops the concept of "gradual parameter interval splitting" to improve the node ordering for different parameter values. The algorithm combines node contraction with a goal-directed technique to further improve performance of flexible queries.
An Effectively Modified Firefly Algorithm for Economic Load Dispatch ProblemTELKOMNIKA JOURNAL
This paper proposes an effectively modified firefly algorithm (EMFA) for searching optimal solution of economic load dispatch (ELD) problem. The proposed method is developed by improving the procedure of new solution generation of conventional firefly algorithm (FA). The performance of EMFA is compared to FA variants and other existing methods by testing on four different systems with different types of objective function and constraints. The comparison indicates that the proposed method can reach better optimal solutions than other FA variants and most other existing methods with lower population and lower maximum iteration. As a result, it can lead to a conclusion that the proposed method is potential for ELD problem.
1) The document presents a particle swarm optimization (PSO) technique to solve economic load dispatch problems in a more computationally efficient manner than genetic algorithms.
2) PSO is a population-based optimization technique that is faster and requires less computation time per iteration than genetic algorithms. It is well-suited for solving complex non-linear optimization problems.
3) The study applies PSO to minimize generation costs for an economic load dispatch problem subject to constraints. Simulation results demonstrate that PSO solves the problem with less computational time and iterations compared to genetic algorithms.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Research Summary: Scalable Algorithms for Nearest-Neighbor Joins on Big Traje...Alex Klibisz
Research summary for my STAT645 course fall 2016. Paper Scalable Algorithms for Nearest-Neighbor Joins on Big Trajectory Data by Fang, Cheng, Tang, Maniu, Yang. http://ieeexplore.ieee.org/document/7498408/
A Non Parametric Estimation Based Underwater Target ClassifierCSCJournals
Underwater noise sources constitute a prominent class of input signal in most underwater signal processing systems. The problem of identification of noise sources in the ocean is of great importance because of its numerous practical applications. In this paper, a methodology is presented for the detection and identification of underwater targets and noise sources based on non parametric indicators. The proposed system utilizes Cepstral coefficient analysis and the Kruskal-Wallis H statistic along with other statistical indicators like F-test statistic for the effective detection and classification of noise sources in the ocean. Simulation results for typical underwater noise data and the set of identified underwater targets are also presented in this paper.
This paper presents a new algorithm called the translational propagation algorithm for generating near-optimal Latin hypercube designs (LHDs) without using formal optimization. The algorithm exploits patterns in optimal LHDs by translating small building blocks consisting of points within the design space. It was found that the algorithm represents a computationally fast strategy for obtaining good LHDs, especially for medium-dimensional design spaces. The algorithm divides the design space into blocks based on the number of points in the seed design and final LHD. It then propagates the seed design through translations to fill the blocks while maintaining Latin hypercube properties. Monte Carlo simulations evaluated the performance of the algorithm for different configurations and compared it to formal optimization approaches.
Multinomial Logistic Regression with Apache SparkDB Tsai
Logistic Regression can not only be used for modeling binary outcomes but also multinomial outcome with some extension. In this talk, DB will talk about basic idea of binary logistic regression step by step, and then extend to multinomial one. He will show how easy it's with Spark to parallelize this iterative algorithm by utilizing the in-memory RDD cache to scale horizontally (the numbers of training data.) However, there is mathematical limitation on scaling vertically (the numbers of training features) while many recent applications from document classification and computational linguistics are of this type. He will talk about how to address this problem by L-BFGS optimizer instead of Newton optimizer.
Bio:
DB Tsai is a machine learning engineer working at Alpine Data Labs. He is recently working with Spark MLlib team to add support of L-BFGS optimizer and multinomial logistic regression in the upstream. He also led the Apache Spark development at Alpine Data Labs. Before joining Alpine Data labs, he was working on large-scale optimization of optical quantum circuits at Stanford as a PhD student.
Approximation Algorithms for the Directed k-Tour and k-Stroll ProblemsSunny Kr
In the Asymmetric Traveling Salesman Problem (ATSP), the input is a directed n-vertex graph G = (V; E) with nonnegative edge lengths, and the goal is to nd a minimum-length tour, visiting
each vertex at least once. ATSP, along with its undirected counterpart, the Traveling Salesman
problem, is a classical combinatorial optimization problem
The best known deterministic polynomial-time algorithm for primality testing right now is due to
Agrawal, Kayal, and Saxena. This algorithm has a time complexity O(log15=2(n)). Although this algorithm is
polynomial, its reliance on the congruence of large polynomials results in enormous computational requirement.
In this paper, we propose a parallelization technique for this algorithm based on message-passing
parallelism together with four workload-distribution strategies. We perform a series of experiments on an
implementation of this algorithm in a high-performance computing system consisting of 15 nodes, each with
4 CPU cores. The experiments indicate that our proposed parallelization technique introduce a significant
speedup on existing implementations. Furthermore, the dynamic workload-distribution strategy performs
better than the others. Overall, the experiments show that the parallelization obtains up to 36 times speedup.
Modern electronic structure codes give relatively consistent equations of state. There remain challenges to fully automating electronic structure calculations, such as developing robust materials analysis software to integrate calculations, detecting and correcting errors, and managing scientific workflows. Frameworks like pymatgen, ASE, the Materials Project, AiiDA and Custodian provide modular, reusable tools for high-throughput electronic structure computations and extensive materials analysis capabilities. FireWorks serves as a workflow manager to automate calculations over diverse supercomputing resources. With automation comes large quantities of materials data that can be leveraged for materials design and discovery.
A first order hyperbolic framework for large strain computational computation...Jibran Haider
An explicit Total Lagrangian momentum-strains mixed formulation in the form of a system of first order hyperbolic conservation laws, has recently been published to overcome the shortcomings posed by the traditional second order displacement based formulation when using linear tetrahedral elements.
The formulation, where the linear momentum and the deformation gradient are treated as unknown variables, has been implemented within the cell centred finite volume environment in OpenFOAM. The numerical solutions have performed extremely well in bending dominated nearly incompressible scenarios without the appearance of any spurious pressure modes, yielding an equal order of convergence for velocities and stresses.
To have more insight into my research, please visit my website:
http://jibranhaider.weebly.com/
A review of literature shows that there is a variety of works studying coverage path planning in several autonomous robotic applications. In this work, we propose a new approach using Markov Decision Process to plan an optimum path to reach the general goal of exploring an unknown environment containing buried mines. This approach, called Goals to Goals Area Coverage on-line Algorithm, is based on a decomposition of the state space into smaller regions whose states are considered as goals with the same reward value, the reward value is decremented from one region to another according to the desired search mode. The numerical simulations show that our approach is promising for minimizing the necessary cost-energy to cover the entire area.
Bi-objective Optimization Apply to Environment a land Economic Dispatch Probl...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
A COMPARISON OF PARTICLE SWARM OPTIMIZATION AND DIFFERENTIAL EVOLUTIONijsc
Two modern optimization methods including Particle Swarm Optimization and Differential Evolution are
compared on twelve constrained nonlinear test functions. Generally, the results show that Differential
Evolution is better than Particle Swarm Optimization in terms of high-quality solutions, running time and
robustness.
This document discusses real-time onset detection in musical signals. It presents various state-of-the-art methods for onset detection, including energy methods, spectral difference methods, and linear prediction methods. These methods work by first calculating onset detection functions, then detecting peaks in those functions and applying thresholding to identify onset locations. The document also discusses a multi-step approach involving onset detection functions, peak detection, and thresholding. It provides details on various methods and observations but does not include results.
RuleML 2015 Constraint Handling Rules - What Else?RuleML
Constraint Handling Rules (CHR) is both a versatile theoretical formalism based on logic and an efficient practical high-level programming language based on rules and constraints.
Procedural knowledge is often expressed by if-then rules, events and actions are related by reaction rules, change is expressed by update rules. Algorithms are often specified using inference rules, rewrite rules, transition rules, sequents, proof rules, or logical axioms. All these kinds of rules can be directly written in CHR. The clean logical semantics of CHR facilitates non-trivial program analysis and transformation. About a dozen implementations of CHR exist in Prolog, Haskell, Java, Javascript and C. Some of them allow to apply millions of rules per second. CHR is also available as WebCHR for online experimentation with more than 40 example programs. More than 200 academic and industrial projects worldwide use CHR, and about 2000 research papers reference it.
The document discusses a maximum likelihood algorithm for accurately estimating the Doppler centroid from SAR data using natural point targets. It begins by motivating the need for an accurate estimation method without using expensive transponders. It then describes (1) using persistent point scatterers as targets, (2) a spotlight azimuth focusing technique to extract target spectra, and (3) maximizing the likelihood function to estimate the Doppler centroid. Results on simulated and real data show the estimate achieves the Cramer-Rao lower bound and improves SAR image quality when applied.
Sampling-Based Planning Algorithms for Multi-Objective MissionsMd Mahbubur Rahman
multiobjective path planning has Increasing demand in military missions, rescue operations, construction job-sites.
There is Lack of robotic path planning algorithm that compromises multiple
objectives. Commonly no solution that optimizes all the objective functions. Here we modify RRT, RRT* sampling based algorithm.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This document presents a hybrid Gravitational Search Algorithm and Sequential Quadratic Programming (GSA-SQP) approach to solve economic emission load dispatch (EELD) problems in power systems. The approach aims to minimize both fuel costs and emission levels simultaneously while satisfying operational constraints. It formulates EELD as a multi-objective optimization problem involving non-linear, non-convex objectives and constraints. Numerical results on three test power systems show the proposed GSA-SQP hybrid approach provides better performing solutions compared to other evolutionary algorithms like NSGA-II and SPEA2.
HyperPrompt:Prompt-based Task-Conditioning of TransformerspdfPo-Chuan Chen
HyperPrompt is a novel architecture that introduces learnable hyper-prompts into the self-attention module of Transformers to enable efficient multi-task learning. HyperPrompt achieves competitive performance compared to strong baselines using only 0.14% additional parameters. It introduces hyper-prompts as global task memories for queries to attend to, and uses hypernetworks to generate layer-specific and task-specific prompts. Experiments on GLUE and SuperGLUE show HyperPrompt outperforms parameter-efficient baselines while maintaining low computational cost for both training and inference.
A Dual Scheme For Traffic Assignment ProblemsAndrew Molina
This document presents a dual scheme method for solving traffic assignment problems. The method uses Lagrangean dualization and subgradient optimization to solve the symmetric traffic equilibrium assignment problem. It has the advantage of computing feasible flow assignments at each iteration that tend toward equilibrium solutions. The Lagrangean subproblem involves shortest path searches. If step lengths in the subgradient procedure follow a modified harmonic series, the average of shortest path flows obtained converges to an equilibrium flow. Computational results show the method performs comparably to Frank-Wolfe and successive averages methods on a medium-sized test problem. The method can also be extended to more complex traffic models.
1) The document presents a particle swarm optimization (PSO) technique to solve economic load dispatch problems in a more computationally efficient manner than genetic algorithms.
2) PSO is a population-based optimization technique that is faster and requires less computation time per iteration than genetic algorithms. It is well-suited for solving complex non-linear optimization problems.
3) The study applies PSO to minimize generation costs for an economic load dispatch problem subject to constraints. Simulation results demonstrate that PSO solves the problem with less computational time and iterations compared to genetic algorithms.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
Research Summary: Scalable Algorithms for Nearest-Neighbor Joins on Big Traje...Alex Klibisz
Research summary for my STAT645 course fall 2016. Paper Scalable Algorithms for Nearest-Neighbor Joins on Big Trajectory Data by Fang, Cheng, Tang, Maniu, Yang. http://ieeexplore.ieee.org/document/7498408/
A Non Parametric Estimation Based Underwater Target ClassifierCSCJournals
Underwater noise sources constitute a prominent class of input signal in most underwater signal processing systems. The problem of identification of noise sources in the ocean is of great importance because of its numerous practical applications. In this paper, a methodology is presented for the detection and identification of underwater targets and noise sources based on non parametric indicators. The proposed system utilizes Cepstral coefficient analysis and the Kruskal-Wallis H statistic along with other statistical indicators like F-test statistic for the effective detection and classification of noise sources in the ocean. Simulation results for typical underwater noise data and the set of identified underwater targets are also presented in this paper.
This paper presents a new algorithm called the translational propagation algorithm for generating near-optimal Latin hypercube designs (LHDs) without using formal optimization. The algorithm exploits patterns in optimal LHDs by translating small building blocks consisting of points within the design space. It was found that the algorithm represents a computationally fast strategy for obtaining good LHDs, especially for medium-dimensional design spaces. The algorithm divides the design space into blocks based on the number of points in the seed design and final LHD. It then propagates the seed design through translations to fill the blocks while maintaining Latin hypercube properties. Monte Carlo simulations evaluated the performance of the algorithm for different configurations and compared it to formal optimization approaches.
Multinomial Logistic Regression with Apache SparkDB Tsai
Logistic Regression can not only be used for modeling binary outcomes but also multinomial outcome with some extension. In this talk, DB will talk about basic idea of binary logistic regression step by step, and then extend to multinomial one. He will show how easy it's with Spark to parallelize this iterative algorithm by utilizing the in-memory RDD cache to scale horizontally (the numbers of training data.) However, there is mathematical limitation on scaling vertically (the numbers of training features) while many recent applications from document classification and computational linguistics are of this type. He will talk about how to address this problem by L-BFGS optimizer instead of Newton optimizer.
Bio:
DB Tsai is a machine learning engineer working at Alpine Data Labs. He is recently working with Spark MLlib team to add support of L-BFGS optimizer and multinomial logistic regression in the upstream. He also led the Apache Spark development at Alpine Data Labs. Before joining Alpine Data labs, he was working on large-scale optimization of optical quantum circuits at Stanford as a PhD student.
Approximation Algorithms for the Directed k-Tour and k-Stroll ProblemsSunny Kr
In the Asymmetric Traveling Salesman Problem (ATSP), the input is a directed n-vertex graph G = (V; E) with nonnegative edge lengths, and the goal is to nd a minimum-length tour, visiting
each vertex at least once. ATSP, along with its undirected counterpart, the Traveling Salesman
problem, is a classical combinatorial optimization problem
The best known deterministic polynomial-time algorithm for primality testing right now is due to
Agrawal, Kayal, and Saxena. This algorithm has a time complexity O(log15=2(n)). Although this algorithm is
polynomial, its reliance on the congruence of large polynomials results in enormous computational requirement.
In this paper, we propose a parallelization technique for this algorithm based on message-passing
parallelism together with four workload-distribution strategies. We perform a series of experiments on an
implementation of this algorithm in a high-performance computing system consisting of 15 nodes, each with
4 CPU cores. The experiments indicate that our proposed parallelization technique introduce a significant
speedup on existing implementations. Furthermore, the dynamic workload-distribution strategy performs
better than the others. Overall, the experiments show that the parallelization obtains up to 36 times speedup.
Modern electronic structure codes give relatively consistent equations of state. There remain challenges to fully automating electronic structure calculations, such as developing robust materials analysis software to integrate calculations, detecting and correcting errors, and managing scientific workflows. Frameworks like pymatgen, ASE, the Materials Project, AiiDA and Custodian provide modular, reusable tools for high-throughput electronic structure computations and extensive materials analysis capabilities. FireWorks serves as a workflow manager to automate calculations over diverse supercomputing resources. With automation comes large quantities of materials data that can be leveraged for materials design and discovery.
A first order hyperbolic framework for large strain computational computation...Jibran Haider
An explicit Total Lagrangian momentum-strains mixed formulation in the form of a system of first order hyperbolic conservation laws, has recently been published to overcome the shortcomings posed by the traditional second order displacement based formulation when using linear tetrahedral elements.
The formulation, where the linear momentum and the deformation gradient are treated as unknown variables, has been implemented within the cell centred finite volume environment in OpenFOAM. The numerical solutions have performed extremely well in bending dominated nearly incompressible scenarios without the appearance of any spurious pressure modes, yielding an equal order of convergence for velocities and stresses.
To have more insight into my research, please visit my website:
http://jibranhaider.weebly.com/
A review of literature shows that there is a variety of works studying coverage path planning in several autonomous robotic applications. In this work, we propose a new approach using Markov Decision Process to plan an optimum path to reach the general goal of exploring an unknown environment containing buried mines. This approach, called Goals to Goals Area Coverage on-line Algorithm, is based on a decomposition of the state space into smaller regions whose states are considered as goals with the same reward value, the reward value is decremented from one region to another according to the desired search mode. The numerical simulations show that our approach is promising for minimizing the necessary cost-energy to cover the entire area.
Bi-objective Optimization Apply to Environment a land Economic Dispatch Probl...ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
A COMPARISON OF PARTICLE SWARM OPTIMIZATION AND DIFFERENTIAL EVOLUTIONijsc
Two modern optimization methods including Particle Swarm Optimization and Differential Evolution are
compared on twelve constrained nonlinear test functions. Generally, the results show that Differential
Evolution is better than Particle Swarm Optimization in terms of high-quality solutions, running time and
robustness.
This document discusses real-time onset detection in musical signals. It presents various state-of-the-art methods for onset detection, including energy methods, spectral difference methods, and linear prediction methods. These methods work by first calculating onset detection functions, then detecting peaks in those functions and applying thresholding to identify onset locations. The document also discusses a multi-step approach involving onset detection functions, peak detection, and thresholding. It provides details on various methods and observations but does not include results.
RuleML 2015 Constraint Handling Rules - What Else?RuleML
Constraint Handling Rules (CHR) is both a versatile theoretical formalism based on logic and an efficient practical high-level programming language based on rules and constraints.
Procedural knowledge is often expressed by if-then rules, events and actions are related by reaction rules, change is expressed by update rules. Algorithms are often specified using inference rules, rewrite rules, transition rules, sequents, proof rules, or logical axioms. All these kinds of rules can be directly written in CHR. The clean logical semantics of CHR facilitates non-trivial program analysis and transformation. About a dozen implementations of CHR exist in Prolog, Haskell, Java, Javascript and C. Some of them allow to apply millions of rules per second. CHR is also available as WebCHR for online experimentation with more than 40 example programs. More than 200 academic and industrial projects worldwide use CHR, and about 2000 research papers reference it.
The document discusses a maximum likelihood algorithm for accurately estimating the Doppler centroid from SAR data using natural point targets. It begins by motivating the need for an accurate estimation method without using expensive transponders. It then describes (1) using persistent point scatterers as targets, (2) a spotlight azimuth focusing technique to extract target spectra, and (3) maximizing the likelihood function to estimate the Doppler centroid. Results on simulated and real data show the estimate achieves the Cramer-Rao lower bound and improves SAR image quality when applied.
Sampling-Based Planning Algorithms for Multi-Objective MissionsMd Mahbubur Rahman
multiobjective path planning has Increasing demand in military missions, rescue operations, construction job-sites.
There is Lack of robotic path planning algorithm that compromises multiple
objectives. Commonly no solution that optimizes all the objective functions. Here we modify RRT, RRT* sampling based algorithm.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
Information Engineering and Technology,
Mechanical, Industrial and Manufacturing Engineering,
Automation and Mechatronics Engineering,
Material and Chemical Engineering,
Civil and Architecture Engineering,
Biotechnology and Bio Engineering,
Environmental Engineering,
Petroleum and Mining Engineering,
Marine and Agriculture engineering,
Aerospace Engineering.
This document presents a hybrid Gravitational Search Algorithm and Sequential Quadratic Programming (GSA-SQP) approach to solve economic emission load dispatch (EELD) problems in power systems. The approach aims to minimize both fuel costs and emission levels simultaneously while satisfying operational constraints. It formulates EELD as a multi-objective optimization problem involving non-linear, non-convex objectives and constraints. Numerical results on three test power systems show the proposed GSA-SQP hybrid approach provides better performing solutions compared to other evolutionary algorithms like NSGA-II and SPEA2.
HyperPrompt:Prompt-based Task-Conditioning of TransformerspdfPo-Chuan Chen
HyperPrompt is a novel architecture that introduces learnable hyper-prompts into the self-attention module of Transformers to enable efficient multi-task learning. HyperPrompt achieves competitive performance compared to strong baselines using only 0.14% additional parameters. It introduces hyper-prompts as global task memories for queries to attend to, and uses hypernetworks to generate layer-specific and task-specific prompts. Experiments on GLUE and SuperGLUE show HyperPrompt outperforms parameter-efficient baselines while maintaining low computational cost for both training and inference.
A Dual Scheme For Traffic Assignment ProblemsAndrew Molina
This document presents a dual scheme method for solving traffic assignment problems. The method uses Lagrangean dualization and subgradient optimization to solve the symmetric traffic equilibrium assignment problem. It has the advantage of computing feasible flow assignments at each iteration that tend toward equilibrium solutions. The Lagrangean subproblem involves shortest path searches. If step lengths in the subgradient procedure follow a modified harmonic series, the average of shortest path flows obtained converges to an equilibrium flow. Computational results show the method performs comparably to Frank-Wolfe and successive averages methods on a medium-sized test problem. The method can also be extended to more complex traffic models.
A Robust Method Based On LOVO Functions For Solving Least Squares ProblemsDawn Cook
The document presents a new robust method for solving least squares problems based on Lower Order-Value Optimization (LOVO) functions. The method combines a Levenberg-Marquardt algorithm adapted for LOVO problems with a voting schema to estimate the number of possible outliers without requiring it as a parameter. Numerical results show the algorithm is able to detect and ignore outliers to find better model fits to data compared to other robust algorithms.
An Exact Branch And Bound Algorithm For The General Quadratic Assignment ProblemJoe Andelija
The document describes an exact branch and bound algorithm for solving the general quadratic assignment problem. It reviews several existing exact algorithms and integer programming formulations for the QAP. The author proposes a new exact algorithm based on linearizing the general QAP into a linear assignment problem that is smaller in size. Computational results and comparisons to other methods are discussed.
A QSAR is a mathematical relationship between a biological activity of a molecular system and its geometric and chemical characteristics.
QSAR attempts to find consistent relationship between biological activity and molecular properties, so that these “rules” can be used to evaluate the activity of new compounds.
News from NNPDF: QED, small-x, and alphas(MZ) fitsjuanrojochacon
Juan Rojo presented recent work from the NNPDF collaboration on three spin-off fits from their NNPDF3.1 global analysis: NNPDF3.1QED, fits including small-x resummation, and a determination of the strong coupling constant αS(mZ). For NNPDF3.1QED, they are imposing the LUXqed formalism to constrain the photon PDF rather than extracting it from data. For small-x resummation fits, they find that including NNLO+NLLx theory stabilizes the small-x gluon and improves description of HERA data. Their preliminary αS(mZ) value is consistent with other determinations.
aMCfast: Automation of Fast NLO Computations for PDF fitsjuanrojochacon
MadGraph5_aMCatNLO provides NLO calculations for arbitrary processes and their matching to parton showers, but existing fast interfaces are limited. A new tool called aMCfast provides a fast interface to MadGraph5_aMCatNLO, allowing its predictions to be used in global PDF fits. It precomputes matrix elements and interpolates them using grids, then reconstructs distributions for any PDFs or scales. This will increase the number and accuracy of processes in PDF fits, including electroweak corrections and photon-initiated effects, improving determination of PDFs from LHC data.
This document summarizes a presentation on tools and protocols for drug design using density functional theory (DFT). It introduces computer-aided drug design and molecular modeling techniques like quantum mechanics, semi-empirical methods, and DFT. Applications of these methods include structure optimization, calculating properties like HOMO-LUMO energies, and molecular docking for drug discovery. Several examples are provided of using DFT calculations to model drug-receptor binding and evaluate compounds for treating diseases.
Molecular docking tools aim to predict the binding mode of ligands to protein receptors. The main tasks are sampling ligand conformations and scoring protein-ligand complexes. Early methods treated proteins and ligands as rigid bodies, while newer methods introduce flexibility. Popular algorithms include Monte Carlo, molecular dynamics, simulated annealing and genetic algorithms. Scoring functions evaluate shape complementarity, empirical potentials, force fields or knowledge-based potentials derived from protein-ligand structures. Consensus scoring integrating multiple functions improves binding affinity prediction over single functions.
Methods available in WIEN2k for the treatment of exchange and correlation ef...ABDERRAHMANE REGGAD
This document summarizes methods available in the WIEN2k software for treating exchange and correlation effects beyond semilocal density functional theory. It discusses the semilocal generalized gradient approximation and meta-GGA functionals, the modified Becke-Johnson potential for improving band gaps, dispersion correction methods, and on-site corrections like DFT+U and hybrid functionals for strongly correlated materials. Input parameters and keywords for selecting these methods in the WIEN2k code are also outlined.
NNPDF3.0: parton distributions for the LHC Run IIjuanrojochacon
NNPDF3.0 is a new PDF determination that includes updated data and theory improvements compared to NNPDF2.3. It includes all HERA-II data and new LHC measurements. The fitting code was rewritten in C++ and validated using closure tests. NNPDF3.0 shows reasonable agreement with NNPDF2.3 while improving descriptions of data and reducing uncertainties in some regions. It provides PDFs for use at the LHC Run II.
This paper proposes a method for adapting the dictionary elements in kernel-based nonlinear adaptive filtering algorithms. The dictionary contains a subset of input vectors that are used to approximate the nonlinear system. Typically, elements are added to the dictionary but never removed or adapted. The proposed method considers dictionary elements as adjustable model parameters that can be optimized to minimize the instantaneous output error, while maintaining coherence to control complexity. Gradient-based adaptation is derived for polynomial and radial basis kernels. Dictionary adaptation is incorporated into Kernel Recursive Least Squares, Kernel Normalized Least Mean Squares, and Kernel Affine Projection algorithms. Experiments on simulated and real data demonstrate that dictionary adaptation can reduce error or dictionary size compared to non-adaptive methods.
This document presents an optimal algorithm for fixed priority scheduling with deferred preemption (FPDS). It first discusses related work on fixed priority scheduling and the motivations for FPDS. It then provides background on FPDS models and defines the system model. The document outlines elements of schedulability analysis for FPDS and provides examples. It describes the high-level FNR algorithm that minimizes final non-preemptive regions. Finally, it proves the optimality of the algorithm and discusses results showing it can find a schedulable solution whenever one exists.
A Research on Optimal Power Flow Solutions For Variable LoaIJERA Editor
This document discusses research on using optimization techniques to solve the optimal power flow problem under variable load conditions. It proposes combining the continuation method with an interior point algorithm to track optimal power flow solutions as the load parameter is increased. This would allow analyzing system behavior near the maximum loadability limit. The research aims to study optimal power flow behavior near limits, evaluate the proposed methodology's efficiency, and analyze critical bus indices and sensitivity of maximum load to reactive power injections. Results show the proposed approach can track solutions continuously for load increases where no new operational limits become active.
An upwind cell centred Finite Volume Method for nearly incompressible explici...Jibran Haider
This document presents a mixed finite volume formulation for simulating explicit solid dynamics problems. It develops a first-order hyperbolic system of conservation laws in a total Lagrangian frame. An upwind cell-centered finite volume method called TOUCH is used to discretize the governing equations. This method is implemented in OpenFOAM to simulate fast transient solid dynamics problems. The methodology aims to bridge the gap between computational fluid dynamics and computational solid dynamics.
The document proposes a new method for approximating matrix finite impulse response (FIR) filters using lower order infinite impulse response (IIR) filters. The method is based on approximating descriptor systems and requires only standard linear algebraic routines. Both optimal and suboptimal cases are addressed in a unified treatment. The solution is derived using only the Markov parameters of the FIR filter and can be expressed in state-space or transfer function form. The effectiveness of the method is illustrated with a numerical example and additional applications are discussed.
Diseño rapido de amplificadores con valoresFélix Chávez
This document describes a tool called GPCAD that optimizes and automates component and transistor sizing for CMOS operational amplifiers. The tool formulates amplifier design problems as geometric programs, a type of convex optimization problem that can be solved very efficiently to determine a globally optimal design. The document discusses how GPCAD applies the geometric programming method to six common op-amp architectures and provides example designs. It also reviews previous approaches to op-amp synthesis and describes the transistor modeling and performance specifications that can be formulated within the geometric programming framework.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skills
Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html
Describing and Interpreting an Immersive Learning Case with the Immersion Cub...Leonel Morgado
Current descriptions of immersive learning cases are often difficult or impossible to compare. This is due to a myriad of different options on what details to include, which aspects are relevant, and on the descriptive approaches employed. Also, these aspects often combine very specific details with more general guidelines or indicate intents and rationales without clarifying their implementation. In this paper we provide a method to describe immersive learning cases that is structured to enable comparisons, yet flexible enough to allow researchers and practitioners to decide which aspects to include. This method leverages a taxonomy that classifies educational aspects at three levels (uses, practices, and strategies) and then utilizes two frameworks, the Immersive Learning Brain and the Immersion Cube, to enable a structured description and interpretation of immersive learning cases. The method is then demonstrated on a published immersive learning case on training for wind turbine maintenance using virtual reality. Applying the method results in a structured artifact, the Immersive Learning Case Sheet, that tags the case with its proximal uses, practices, and strategies, and refines the free text case description to ensure that matching details are included. This contribution is thus a case description method in support of future comparative research of immersive learning cases. We then discuss how the resulting description and interpretation can be leveraged to change immersion learning cases, by enriching them (considering low-effort changes or additions) or innovating (exploring more challenging avenues of transformation). The method holds significant promise to support better-grounded research in immersive learning.
The binding of cosmological structures by massless topological defectsSérgio Sacani
Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field
equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational
field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin
spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling
concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect
light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is
mitigated, at least in part.
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
Authoring a personal GPT for your research and practice: How we created the Q...Leonel Morgado
Thematic analysis in qualitative research is a time-consuming and systematic task, typically done using teams. Team members must ground their activities on common understandings of the major concepts underlying the thematic analysis, and define criteria for its development. However, conceptual misunderstandings, equivocations, and lack of adherence to criteria are challenges to the quality and speed of this process. Given the distributed and uncertain nature of this process, we wondered if the tasks in thematic analysis could be supported by readily available artificial intelligence chatbots. Our early efforts point to potential benefits: not just saving time in the coding process but better adherence to criteria and grounding, by increasing triangulation between humans and artificial intelligence. This tutorial will provide a description and demonstration of the process we followed, as two academic researchers, to develop a custom ChatGPT to assist with qualitative coding in the thematic data analysis process of immersive learning accounts in a survey of the academic literature: QUAL-E Immersive Learning Thematic Analysis Helper. In the hands-on time, participants will try out QUAL-E and develop their ideas for their own qualitative coding ChatGPT. Participants that have the paid ChatGPT Plus subscription can create a draft of their assistants. The organizers will provide course materials and slide deck that participants will be able to utilize to continue development of their custom GPT. The paid subscription to ChatGPT Plus is not required to participate in this workshop, just for trying out personal GPTs during it.
Immersive Learning That Works: Research Grounding and Paths ForwardLeonel Morgado
We will metaverse into the essence of immersive learning, into its three dimensions and conceptual models. This approach encompasses elements from teaching methodologies to social involvement, through organizational concerns and technologies. Challenging the perception of learning as knowledge transfer, we introduce a 'Uses, Practices & Strategies' model operationalized by the 'Immersive Learning Brain' and ‘Immersion Cube’ frameworks. This approach offers a comprehensive guide through the intricacies of immersive educational experiences and spotlighting research frontiers, along the immersion dimensions of system, narrative, and agency. Our discourse extends to stakeholders beyond the academic sphere, addressing the interests of technologists, instructional designers, and policymakers. We span various contexts, from formal education to organizational transformation to the new horizon of an AI-pervasive society. This keynote aims to unite the iLRN community in a collaborative journey towards a future where immersive learning research and practice coalesce, paving the way for innovative educational research and practice landscapes.
ESA/ACT Science Coffee: Diego Blas - Gravitational wave detection with orbita...Advanced-Concepts-Team
Presentation in the Science Coffee of the Advanced Concepts Team of the European Space Agency on the 07.06.2024.
Speaker: Diego Blas (IFAE/ICREA)
Title: Gravitational wave detection with orbital motion of Moon and artificial
Abstract:
In this talk I will describe some recent ideas to find gravitational waves from supermassive black holes or of primordial origin by studying their secular effect on the orbital motion of the Moon or satellites that are laser ranged.
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...AbdullaAlAsif1
The pygmy halfbeak Dermogenys colletei, is known for its viviparous nature, this presents an intriguing case of relatively low fecundity, raising questions about potential compensatory reproductive strategies employed by this species. Our study delves into the examination of fecundity and the Gonadosomatic Index (GSI) in the Pygmy Halfbeak, D. colletei (Meisner, 2001), an intriguing viviparous fish indigenous to Sarawak, Borneo. We hypothesize that the Pygmy halfbeak, D. colletei, may exhibit unique reproductive adaptations to offset its low fecundity, thus enhancing its survival and fitness. To address this, we conducted a comprehensive study utilizing 28 mature female specimens of D. colletei, carefully measuring fecundity and GSI to shed light on the reproductive adaptations of this species. Our findings reveal that D. colletei indeed exhibits low fecundity, with a mean of 16.76 ± 2.01, and a mean GSI of 12.83 ± 1.27, providing crucial insights into the reproductive mechanisms at play in this species. These results underscore the existence of unique reproductive strategies in D. colletei, enabling its adaptation and persistence in Borneo's diverse aquatic ecosystems, and call for further ecological research to elucidate these mechanisms. This study lends to a better understanding of viviparous fish in Borneo and contributes to the broader field of aquatic ecology, enhancing our knowledge of species adaptations to unique ecological challenges.
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptxMAGOTI ERNEST
Although Artemia has been known to man for centuries, its use as a food for the culture of larval organisms apparently began only in the 1930s, when several investigators found that it made an excellent food for newly hatched fish larvae (Litvinenko et al., 2023). As aquaculture developed in the 1960s and ‘70s, the use of Artemia also became more widespread, due both to its convenience and to its nutritional value for larval organisms (Arenas-Pardo et al., 2024). The fact that Artemia dormant cysts can be stored for long periods in cans, and then used as an off-the-shelf food requiring only 24 h of incubation makes them the most convenient, least labor-intensive, live food available for aquaculture (Sorgeloos & Roubach, 2021). The nutritional value of Artemia, especially for marine organisms, is not constant, but varies both geographically and temporally. During the last decade, however, both the causes of Artemia nutritional variability and methods to improve poorquality Artemia have been identified (Loufi et al., 2024).
Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
1. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Systematic comparison between non-perturbative
functional methods in low-energy QCD models
Jordi Par´ıs L´opez
Advisors: R. Alkofer and H. Sanchis-Alepuz
Karl-Franzens-Universit¨at Graz, Austria
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 1 / 33
2. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Content
Motivation and thesis objectives.
Basics of the functional methods.
Results using the Functional Renormalisation Group (FRG).
Comparison between functional methods.
Summary.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 2 / 33
3. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Motivation and thesis objectives
Many features from QCD still not completely understood.
Bound states inherently non-perturbative.
Large couplings in QCD at hadronic energies.
Non-perturbative approaches required → Functional Methods.
No sign problem.
Wide range of scales.
Successful predictions in QCD: Observables, DχSB,...
Different truncations and approximations.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 3 / 33
4. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Functional methods treated:
Dyson-Schwinger–Bethe-Salpeter equations (DSE-BSE).
Functional Renormalisation Group (FRG).
Objectives
Obtain observables using the FRG in different approximations.
Compare both approaches in different low-energy QCD models.
Analyse viability of the methods: truncations, numerics, etc.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 4 / 33
5. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Basics of functional methods
Euclidean generating functional as starting point:
Z[J] = eW[J]
= Dφ e−S[φ]+ x Jφ
Effective Action Γ[φ] from W[J] Legendre transformation:
e−Γ[ϕ]
= Dφ exp −S[ϕ + φ] +
x
dΓ[ϕ]
dϕ
φ
with δΓ
δϕ ≡ J , ϕ ≡ δW[J]
δJ = φ J .
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 5 / 33
6. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
The effective action Γ[φ]:
Expressed as sum of 1PI Green’s functions.
Main object of interest in functional methods.
Calculation of Γ[φ] using functional equations:
DSE: coupled integral equations.
FRG: differential equations containing integrals.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 6 / 33
7. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
The Functional Renormalisation Group (FRG)1
Main functional: scale dependent 1-PI effective action: Γ[φ] → Γk[φ].
Scale introduced via regulator ∆Sk[φ].
Initial and final conditions are fixed in theory space:
Γk=Λ ≃ Sbare
Γk≃0 ≡ Γ
The choice of the regulator is not unique.
1
See, e.g., Gies, arXiv:hep-ph/0611146 for an introduction.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 7 / 33
8. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Using quadratic regulators ∆Sk[φ] = p φRkφ:
∂tΓk =
1
2
Tr ∂tRk Γ
(2)
k + Rk
−1
Wetterich’s Flow Equation
with t = ln k
Λ and ∂t = k∂k.
Euclidean non-perturbative 1-loop integral-differential equation.
Leads to non-perturbative flow equation for vertex functions:
−1
=∂t + + +
Truncation/approximation required.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 8 / 33
9. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Dynamical hadronisation
Convenient to work with macroscopic QCD degrees of freedom.
Mesons introduced from a 4-Fermi interaction via the
Hubbard-Stratonovich (HS) transformation.
Problem: non-zero 4-Fermi interaction flow ∂tλk
=⇒ HS transformation cancelled in every RG-step:
∂t = + . . .
Solved by dynamical hadronisation.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 9 / 33
10. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Introduction of scale dependent bosonic field:
∂tφk = ∂tAk( ¯ψτψ)
Wetterich’s flow equation modified =⇒ Additional term in ∂tλk:
∂tλk = Flow λk − hk∂tAk
!
= 0
Generalisation of HS transformation for every RG-step.
Green’s functions computed with meson exchange diagrams:
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 10 / 33
11. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Results using the FRG
Gluons decoupled at low energies2. Low-energy QCD effectively described
by fermionic NJL-like models. Mesons introduced via HS transformation.
Approximate effective action of the Quark Meson model:
Γk
¯ψ, ψ, σ, π = Γ
(int)
k,4ψ [ ¯ψ, ψ] +
p
Zk,ψ
¯ψ i/p ψ +
+
1
2
p2 Zk,σ σ2 + Zk,π π2 + Vk[σ, π] − cσ +
+
q
hk
¯ψ
σ
2
+ iγ5τzπz
ψ
2
Comparison to the full calculation, see A.Cyrol et al, arXiv:1605.01856.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 11 / 33
12. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Multi-meson interactions introduced via O(N) potential following:
Vk(ρ) =
∞
n=0
V
(n)
k
n!
(ρ − ρ0)n
with ρ = 1
2 σ2 + π2 and ρ0 scale independent expansion point.
Flow equations to solve:
Potential terms, ˙V
(i)
k with i = 0, ... , 8.
Wave function renormalisation, ˙Zk,i with i = σ, π, ψ.
4-Fermi coupling, ˙λk = Flow λk − hk
˙Ak ≡ 0.
Yukawa coupling, ˙hk = Flow hk − V
(1)
k
˙Ak.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 12 / 33
13. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Approximations used:
LPA: Scale-dependent potential, constant Yukawa coupling
hk(p2) = h, unit Zk,i(p2) = 1 and zero 4-Fermi coupling λk = 0.
LPA+Y: Yukawa coupling includes scale dependence.
LPA+Y’: Yukawa coupling includes scale and momentum
dependence.
Full: Scale and momentum-dependent wave function renormalisations
Zk,i(p2) are included.
Full+DH: Dynamical hadronisation taken into account.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 13 / 33
14. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
0.0 0.2 0.4 0.6 0.8 1.0
k (GeV)
0.5
1.0
1.5
2.0
2.5
¯mk(GeV)
Pion
Sigma Meson
LPA
LPA+Y
LPA+Y’
Full
Full+DH
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 14 / 33
15. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
0.0 0.2 0.4 0.6 0.8 1.0
k (GeV)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
¯mk,ψ(GeV)
LPA
LPA+Y
LPA+Y’
Full
Full+DH
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 15 / 33
16. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75
p (GeV)
0.25
0.26
0.27
0.28
0.29
0.30
¯mIR,ψ(GeV)
LPA+Y’
Full
Full+DH
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 16 / 33
18. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Applying analytic continuation to obtain pole masses and comparing with
curvature ”masses” (CM) mk,i we obtained:
Particle CM (Input) Pole Mass Decay Width
Pion 138.053 137.6 ± 0.4 0.5 ± 0.5
Sigma meson 551.843 330 ± 15 30 ± 6
Table: Pole masses vs. curvature masses and decay widths, all in MeV.
Pion pole mass agrees with CM, decay width compatible with zero.
Sigma meson pole mass close to two pion decay threshold, pole
belonging to second Riemann sheet.
Analytic continuation used requires large number of data points.
Results compatible with QCD calculations.3
3
Comparison with fQCD calculations, see Alkofer et al, arXiv:1810.07955.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 18 / 33
19. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Comparison between functional methods
Formal comparison.
Practical comparison in truncated low-energy QCD models.
Nambu-Jona-Lasinio (NJL) model.
Gross-Neveu (GN) model.
Quark-Meson (QM) model.
Numerical comparison.
Intrinsic properties of the methods.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 19 / 33
20. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Dyson-Schwinger equations (DSEs)
Consequence from cancellation of path integral under total derivative:
Dφ
δ
δφ
e−S[φ]+ x Jφ
= 0
DSEs for 1PI correlators:
δΓ[ϕ]
δϕi
−
δS
δϕi
ϕ +
δ2Γ[ϕ]
δϕδϕj
−1
δ
δϕj
= 0
Self-coupled integral equations not exactly solvable in general.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 20 / 33
21. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
DSEs in QCD:
−1−1
=
=
Quark Propagator
+
+
++
Quark-Gluon Vertex
...
Infinite tower of coupled equations.
Truncation is required.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 21 / 33
23. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Bethe-Salpeter equation: bound state equation for mesons:
Γ = KG0Γ
Pion BSE under Rainbow-Ladder truncation:
q q~
kq P P=
Γ Γ
−0.20 −0.15 −0.10 −0.05 0.00
p2 (GeV)
0.96
0.98
1.00
1.02
1.04
λ
−0.25 −0.20 −0.15 −0.10 −0.05 0.00
p2 (GeV)
−2000
−1500
−1000
−500
0
500
1000
1500
2000
f(0)
(p2
,0,0)
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 23 / 33
24. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
The NJL model
Fermion system with 4-Fermi interaction:
S[ ¯ψ, ψ] =
p
¯ψ(i/p + mq)ψ + λ ¯ψψ
2
Diagrammatic equations:
−1
−1−1
=
=
∂t
Quark DSE
+ +
Quark flow equation
+
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 24 / 33
25. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Same analytical expression obtained:
Proper interpretation of scale-dependent parameters.
Using constant λ ∝ c
Λ2 approximation.
0 1 2 3 4 5
c
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
M(GeV)
mq = 0
mq = 0
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 25 / 33
26. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
The GN model
Fermion system with 4-Fermi interaction in 2-dimensions:
S[ ¯ψ, ψ] =
d2p
(2π)2
¯ψ(i/p + mq)ψ + λ ¯ψψ
2
System is renormalisable.
Quark propagator dressings get momentum dependence.
2-loop terms appear.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 26 / 33
27. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
−1−1
−1
=
=
=
=
∂t
∂t
DSE
+ + +
+ + + + +
+
+ + +
+ + +
+
FRG
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a
a
a aaaa
aaaa
b
bb
b
b
b
b
b
b
b
b
b
b
b
c
cc
c
c
c
c
ccc
c
ccc
ddd
d
d
d dd
d
d
dd
d
d
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 27 / 33
28. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
10−3
10−2
10−1
100
101
102
103
104
105
p2
(GeV)
2
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
M(p2
)(GeV)
FRG
DSE
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 28 / 33
29. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
The Quark-Meson model
Bare action from bosonised NJL model:
S[ψ, ¯ψ, σ, π] =
p
¯ψ Z2 i/p ψ +
m2
2
Zσ σ2
+ Zπ π2
+
q
¯ψh
Zhσ
2
σ + i Zhπ γ5 τ π ψ
No bosonic kinetic terms.
Momentum-dependent quantities generated dynamically.
Self-coupled system of equations with zero quark-multi-meson vertex.
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 29 / 33
31. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Intrinsic properties of the FRG
Dynamically generated kinetic terms.
Propagating degrees of freedom are preserved.
Probability amplitude conservation during flow:
Z−2
k,ψ +
1
4
Z2
k,σ +
3
4
Z2
k,π ≡ Zk,s = 1 ∀k
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 31 / 33
32. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
0.0 0.2 0.4 0.6 0.8
k (GeV)
0.0
0.2
0.4
0.6
0.8
1.0
WaveFunctionRenormalisation
Z−1
k,ψ
Zk,π
Zk,σ
Zk,s
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 32 / 33
33. Motivation and objectives Basics of functional methods Results using the FRG DSE-FRG comparison Summary
Summary
The FRG provides an alternative procedure to the BSE/Faddeev
equation to obtain resonance masses and decay widths.
Observables obtained are compatible with physical processes.
Approximations compatible in both functional methods can be found,
relating FRG with DSEs and BSEs.
The FRG reduces complexity of equations by introducing an
additional parameter.
Sophisticated numerical tools required in both functional methods.
THANK YOU FOR YOUR ATTENTION
Jordi Par´ıs L´opez Systematic comparison between functional methods in low-energy QCD 33 / 33