scholarly journals Projection Path Explorer: Exploring Visual Patterns in Projected Decision-making Paths

2021 ◽  
Vol 11 (3-4) ◽  
pp. 1-29
Author(s):  
Andreas Hinterreiter ◽  
Christian Steinparz ◽  
Moritz SchÖfl ◽  
Holger Stitz ◽  
Marc Streit
Keyword(s):  
Problem Solving ◽  
Optimization Problems ◽  
Initial Conditions ◽  
Dimensional Space ◽  
Dimensional Representation ◽  
Self Similarity ◽  
Solution Strategies ◽  
Network Training ◽  
Strategy Games ◽  
Lower Dimensional Space

In problem-solving, a path towards a solutions can be viewed as a sequence of decisions. The decisions, made by humans or computers, describe a trajectory through a high-dimensional representation space of the problem. By means of dimensionality reduction, these trajectories can be visualized in lower-dimensional space. Such embedded trajectories have previously been applied to a wide variety of data, but analysis has focused almost exclusively on the self-similarity of single trajectories. In contrast, we describe patterns emerging from drawing many trajectories—for different initial conditions, end states, and solution strategies—in the same embedding space. We argue that general statements about the problem-solving tasks and solving strategies can be made by interpreting these patterns. We explore and characterize such patterns in trajectories resulting from human and machine-made decisions in a variety of application domains: logic puzzles (Rubik’s cube), strategy games (chess), and optimization problems (neural network training). We also discuss the importance of suitably chosen representation spaces and similarity metrics for the embedding.

scholarly journals High Resolution, High Contrast Beamformer Using Minimum Variance and Plane Wave Nonlinear Compounding with Low Complexity

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 394
Author(s):  
Xin Yan ◽  
Yanxing Qi ◽  
Yinmeng Wang ◽  
Yuanyuan Wang
Keyword(s):  
Plane Wave ◽  
Dimensional Space ◽  
Contrast Ratio ◽  
Low Complexity ◽  
Minimum Variance ◽  
Frame Rate ◽  
Channel Noise ◽  
Length Estimation ◽  
Lower Dimensional Space

The plane wave compounding (PWC) is a promising modality to improve the imaging quality and maintain the high frame rate for ultrafast ultrasound imaging. In this paper, a novel beamforming method is proposed to achieve higher resolution and contrast with low complexity. A minimum variance (MV) weight calculated by the partial generalized sidelobe canceler is adopted to beamform the receiving array signals. The dimension reduction technique is introduced to project the data into lower dimensional space, which also contributes to a large subarray length. Estimation of multi-wave receiving covariance matrix is performed and then utilized to determine only one weight. Afterwards, a fast second-order reformulation of the delay multiply and sum (DMAS) is developed as nonlinear compounding to composite the beamforming output of multiple transmissions. Simulations, phantom, in vivo, and robustness experiments were carried out to evaluate the performance of the proposed method. Compared with the delay and sum (DAS) beamformer, the proposed method achieved 86.3% narrower main lobe width and 112% higher contrast ratio in simulations. The robustness to the channel noise of the proposed method is effectively enhanced at the same time. Furthermore, it maintains a linear computational complexity, which means that it has the potential to be implemented for real-time response.

Boosting branch-and-bound MaxSAT solvers with clause learning

2021 ◽  
pp. 1-21
Author(s):  
Chu-Min Li ◽  
Zhenxing Xu ◽  
Jordi Coll ◽  
Felip Manyà ◽  
Djamal Habet ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Combinatorial Optimization ◽  
Problem Solving ◽  
Branch And Bound ◽  
Real World ◽  
Optimization Problems ◽  
Satisfiability Problem ◽  
Maximum Satisfiability ◽  
Combinatorial Optimization Problems ◽  
Clause Learning

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

Spectral analysis of forced turbulence in a non-neutral plasma

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
S. Chen ◽  
G. Maero ◽  
M. Romé
Keyword(s):  
Initial Conditions ◽  
Initial Density ◽  
Final States ◽  
Self Similarity ◽  
Subsequent Formation ◽  
Electron Plasmas ◽  
Particle In Cell ◽  
Fluid Turbulence ◽  
Inviscid Incompressible Fluid ◽  
Forced Turbulence

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

Has a fully three-dimensional space map never evolved in any species? A comparative imperative for studies of spatial cognition

2013 ◽  
Vol 36 (5) ◽  
pp. 557-557 ◽  
Author(s):  
Cynthia F. Moss
Keyword(s):  
Spatial Cognition ◽  
Dimensional Space ◽  
Large Body ◽  
Three Dimensional ◽  
Comparative Data ◽  
Dimensional Representation ◽  
Three Dimensional Representation ◽  
Space Coding ◽  
Three Dimensional Space

AbstractI propose that it is premature to assert that a fully three-dimensional map has never evolved in any species, as data are lacking to show that space coding in all animals is the same. Instead, I hypothesize that three-dimensional representation is tied to an animal's mode of locomotion through space. Testing this hypothesis requires a large body of comparative data.

scholarly journals Why Does Large Batch Training Result in Poor Generalization? A Comprehensive Explanation and a Better Strategy from the Viewpoint of Stochastic Optimization

2018 ◽  
Vol 30 (7) ◽  
pp. 2005-2023 ◽  
Author(s):  
Tomoumi Takase ◽  
Satoshi Oyama ◽  
Masahito Kurihara
Keyword(s):  
Gradient Descent ◽  
Optimization Problems ◽  
Descent Method ◽  
Batch Size ◽  
Gradient Descent Method ◽  
Neural Network Training ◽  
Nonconvex Optimization Problems ◽  
Large Batch ◽  
Network Training ◽  
Comprehensive Framework

We present a comprehensive framework of search methods, such as simulated annealing and batch training, for solving nonconvex optimization problems. These methods search a wider range by gradually decreasing the randomness added to the standard gradient descent method. The formulation that we define on the basis of this framework can be directly applied to neural network training. This produces an effective approach that gradually increases batch size during training. We also explain why large batch training degrades generalization performance, which previous studies have not clarified.

Selecting and Sequencing Students' Solution Strategies

2016 ◽  
Vol 23 (4) ◽  
pp. 226-234 ◽  
Author(s):  
Erin M. Meikle
Keyword(s):  
Problem Solving ◽  
Solution Strategies ◽  
Class Discussions ◽  
Challenging Tasks ◽  
Whole Class ◽  
Fine Tune

For orchestrating whole-class discussions, note these suggestions to fine tune problem-solving techniques into cognitively challenging tasks.

scholarly journals AN OVERVIEW OF SWARM INTELLIGENCE IN ARTIFICIAL INTELLIGENT SYSTEMS

2021 ◽  
Vol 9 (08) ◽  
pp. 673-675
Author(s):  
Kalpana C. Dalwai ◽  
Keyword(s):  
Information Processing ◽  
Problem Solving ◽  
Swarm Intelligence ◽  
Intelligent Systems ◽  
Optimization Problems ◽  
Artificial Intelligent

Swarm intelligence refers to a kind of problem-solving ability that emerges in the interactions of simple information-processing units. The concept of a swarm suggests multiplicity, stochasticity, randomness, and messiness. Advancement of technology has led to problems that are complex and more challenging.Swarm intelligence techniques were mostly developed for solving optimization problems.

scholarly journals Optimization of the multidimensional signal interpolator in a lower dimensional space

2019 ◽  
Vol 43 (4) ◽  
pp. 653-660 ◽  
Author(s):  
M.V. Gashnikov
Keyword(s):  
Experimental Study ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Signal Sample ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Selection Of

Adaptive multidimensional signal interpolators are developed. These interpolators take into account the presence and direction of boundaries of flat signal regions in each local neighborhood based on the automatic selection of the interpolating function for each signal sample. The selection of the interpolating function is performed by a parameterized rule, which is optimized in a parametric lower dimensional space. The dimension reduction is performed using rank filtering of local differences in the neighborhood of each signal sample. The interpolating functions of adaptive interpolators are written for the multidimensional, three-dimensional and two-dimensional cases. The use of adaptive interpolators in the problem of compression of multidimensional signals is also considered. Results of an experimental study of adaptive interpolators for real multidimensional signals of various types are presented.

scholarly journals GENETIC ALGORITHMS FOR MULTIDIMENSIONAL SCALING / GENETINIŲ ALGORITMŲ TAIKYMAS DAUGIAMATĖMS SKALĖMS

2015 ◽  
Vol 7 (3) ◽  
pp. 275-279 ◽  
Author(s):  
Agnė Dzidolikaitė
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Multidimensional Scaling ◽  
Optimization Problem ◽  
Dimensional Space ◽  
Local Solution ◽  
Multidimensional Data ◽  
Global Optimization Problem ◽  
Lower Dimensional Space ◽  
Lower Dimensional

The paper analyzes global optimization problem. In order to solve this problem multidimensional scaling algorithm is combined with genetic algorithm. Using multidimensional scaling we search for multidimensional data projections in a lower-dimensional space and try to keep dissimilarities of the set that we analyze. Using genetic algorithms we can get more than one local solution, but the whole population of optimal points. Different optimal points give different images. Looking at several multidimensional data images an expert can notice some qualities of given multidimensional data. In the paper genetic algorithm is applied for multidimensional scaling and glass data is visualized, and certain qualities are noticed. Analizuojamas globaliojo optimizavimo uždavinys. Jis apibrėžiamas kaip netiesinės tolydžiųjų kintamųjų tikslo funkcijos optimizavimas leistinojoje srityje. Optimizuojant taikomi įvairūs algoritmai. Paprastai taikant tikslius algoritmus randamas tikslus sprendinys, tačiau tai gali trukti labai ilgai. Dažnai norima gauti gerą sprendinį per priimtiną laiko tarpą. Tokiu atveju galimi kiti – euristiniai, algoritmai, kitaip dar vadinami euristikomis. Viena iš euristikų yra genetiniai algoritmai, kopijuojantys gyvojoje gamtoje vykstančią evoliuciją. Sudarant algoritmus naudojami evoliuciniai operatoriai: paveldimumas, mutacija, selekcija ir rekombinacija. Taikant genetinius algoritmus galima rasti pakankamai gerus sprendinius tų uždavinių, kuriems nėra tikslių algoritmų. Genetiniai algoritmai taip pat taikytini vizualizuojant duomenis daugiamačių skalių metodu. Taikant daugiamates skales ieškoma daugiamačių duomenų projekcijų mažesnio skaičiaus matmenų erdvėje siekiant išsaugoti analizuojamos aibės panašumus arba skirtingumus. Taikant genetinius algoritmus gaunamas ne vienas lokalusis sprendinys, o visa optimumų populiacija. Skirtingi optimumai atitinka skirtingus vaizdus. Matydamas kelis daugiamačių duomenų variantus, ekspertas gali įžvelgti daugiau daugiamačių duomenų savybių. Straipsnyje genetinis algoritmas pritaikytas daugiamatėms skalėms. Parodoma, kad daugiamačių skalių algoritmą galima kombinuoti su genetiniu algoritmu ir panaudoti daugiamačiams duomenims vizualizuoti.

scholarly journals Characterization of the Transient Response of Coupled Optimization in Multidisciplinary Design

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Erich Devendorf ◽  
Kemper Lewis
Keyword(s):  
Optimization Problems ◽  
Initial Conditions ◽  
Systems Design ◽  
Discrete Systems ◽  
Product Development Process ◽  
Multidisciplinary Design ◽  
Distributed Design ◽  
Equilibrium Solutions ◽  
Acceptable Solution ◽  
Number Of Iterations

Time is an asset of critical importance in a multidisciplinary design process and it is desirable to reduce the amount of time spent designing products and systems. Design is an iterative activity and designers consume a significant portion of the product development process negotiating a mutually acceptable solution. The amount of time necessary to complete a design depends on the number and duration of design iterations. This paper focuses on accurately characterizing the number of iterations required for designers to converge to an equilibrium solution in distributed design processes. In distributed design, systems are decomposed into smaller, coupled design problems where individual designers have control over local design decisions and seek to achieve their own individual objectives. These smaller coupled design optimization problems can be modeled using coupled games and the number of iterations required to reach equilibrium solutions varies based on initial conditions and process architecture. In this paper, we leverage concepts from game theory, classical controls, and discrete systems theory to evaluate and approximate process architectures without carrying out any solution iterations. As a result, we develop an analogy between discrete decisions and a continuous time representation that we analyze using control theoretic techniques.

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