common representation
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2022 ◽  
Vol 4 ◽  
Author(s):  
Reuth Mirsky ◽  
Ran Galun ◽  
Kobi Gal ◽  
Gal Kaminka

Plan recognition deals with reasoning about the goals and execution process of an actor, given observations of its actions. It is one of the fundamental problems of AI, applicable to many domains, from user interfaces to cyber-security. Despite the prevalence of these approaches, they lack a standard representation, and have not been compared using a common testbed. This paper provides a first step towards bridging this gap by providing a standard plan library representation that can be used by hierarchical, discrete-space plan recognition and evaluation criteria to consider when comparing plan recognition algorithms. This representation is comprehensive enough to describe a variety of known plan recognition problems and can be easily used by existing algorithms in this class. We use this common representation to thoroughly compare two known approaches, represented by two algorithms, SBR and Probabilistic Hostile Agent Task Tracker (PHATT). We provide meaningful insights about the differences and abilities of these algorithms, and evaluate these insights both theoretically and empirically. We show a tradeoff between expressiveness and efficiency: SBR is usually superior to PHATT in terms of computation time and space, but at the expense of functionality and representational compactness. We also show how different properties of the plan library affect the complexity of the recognition process, regardless of the concrete algorithm used. Lastly, we show how these insights can be used to form a new algorithm that outperforms existing approaches both in terms of expressiveness and efficiency.


2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Hitomi Kuranaga ◽  
Hiroshi Ohki ◽  
Shohei Uemura

Abstract We study Froggatt-Nielsen (FN) like flavor models with modular symmetry. The FN mechanism is a convincing solution to the flavor puzzle in the quark sector. The FN mechanism requires an extra U(1) gauge symmetry which is broken at high energies. Alternatively, in the framework of modular symmetry the modular weights can play the role of the FN charges of the extra U(1) symmetry. Based on the FN-like mechanism with modular symmetry we present new flavor models for the quark sector. Assuming that the three generations have a common representation under the modular symmetry, our models simply reproduce the FN-like Yukawa matrices. We also show that the realistic mass hierarchy and mixing angles, which are related to each other through the modular parameters and a scalar vev, can be realized in models with several finite modular groups (and their double covering groups) without unnatural hierarchical parameters.


2021 ◽  
Vol 15 ◽  
Author(s):  
Alessandro Benedetto ◽  
Gabriel Baud-Bovy

Humans possess the ability to extract highly organized perceptual structures from sequences of temporal stimuli. For instance, we can organize specific rhythmical patterns into hierarchical, or metrical, systems. Despite the evidence of a fundamental influence of the motor system in achieving this skill, few studies have attempted to investigate the organization of our motor representation of rhythm. To this aim, we studied—in musicians and non-musicians—the ability to perceive and reproduce different rhythms. In a first experiment participants performed a temporal order-judgment task, for rhythmical sequences presented via auditory or tactile modality. In a second experiment, they were asked to reproduce the same rhythmic sequences, while their tapping force and timing were recorded. We demonstrate that tapping force encodes the metrical aspect of the rhythm, and the strength of the coding correlates with the individual’s perceptual accuracy. We suggest that the similarity between perception and tapping-force organization indicates a common representation of rhythm, shared between the perceptual and motor systems.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Wenyun Gao ◽  
Sheng Dai ◽  
Stanley Ebhohimhen Abhadiomhen ◽  
Wei He ◽  
Xinghui Yin

Correlation learning is a technique utilized to find a common representation in cross-domain and multiview datasets. However, most existing methods are not robust enough to handle noisy data. As such, the common representation matrix learned could be influenced easily by noisy samples inherent in different instances of the data. In this paper, we propose a novel correlation learning method based on a low-rank representation, which learns a common representation between two instances of data in a latent subspace. Specifically, we begin by learning a low-rank representation matrix and an orthogonal rotation matrix to handle the noisy samples in one instance of the data so that a second instance of the data can linearly reconstruct the low-rank representation. Our method then finds a similarity matrix that approximates the common low-rank representation matrix much better such that a rank constraint on the Laplacian matrix would reveal the clustering structure explicitly without any spectral postprocessing. Extensive experimental results on ORL, Yale, Coil-20, Caltech 101-20, and UCI digits datasets demonstrate that our method has superior performance than other state-of-the-art compared methods in six evaluation metrics.


2020 ◽  
Vol 30 (6) ◽  
pp. 2885-2923
Author(s):  
Robert J. Martin ◽  
Jendrik Voss ◽  
Ionel-Dumitrel Ghiba ◽  
Oliver Sander ◽  
Patrizio Neff

Abstract We consider conformally invariant energies W on the group $${{\,\mathrm{GL}\,}}^{\!+}(2)$$ GL + ( 2 ) of $$2\times 2$$ 2 × 2 -matrices with positive determinant, i.e., $$W:{{\,\mathrm{GL}\,}}^{\!+}(2)\rightarrow {\mathbb {R}}$$ W : GL + ( 2 ) → R such that $$\begin{aligned} W(A\, F\, B) = W(F) \quad \text {for all }\; A,B\in \{a\, R\in {{\,\mathrm{GL}\,}}^{\!+}(2) \,|\,a\in (0,\infty ),\; R\in {{\,\mathrm{SO}\,}}(2)\}, \end{aligned}$$ W ( A F B ) = W ( F ) for all A , B ∈ { a R ∈ GL + ( 2 ) | a ∈ ( 0 , ∞ ) , R ∈ SO ( 2 ) } , where $${{\,\mathrm{SO}\,}}(2)$$ SO ( 2 ) denotes the special orthogonal group and provides an explicit formula for the (notoriously difficult to compute) quasiconvex envelope of these functions. Our results, which are based on the representation $$W(F)=h\bigl (\frac{\lambda _1}{\lambda _2}\bigr )$$ W ( F ) = h ( λ 1 λ 2 ) of W in terms of the singular values $$\lambda _1,\lambda _2$$ λ 1 , λ 2 of F, are applied to a number of example energies in order to demonstrate the convenience of the singular-value-based expression compared to the more common representation in terms of the distortion $${\mathbb {K}}:=\frac{1}{2}\frac{\Vert F \Vert ^2}{\det F}$$ K : = 1 2 ‖ F ‖ 2 det F . Applying our results, we answer a conjecture by Adamowicz (in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Serie IX. Matematica e Applicazioni, vol 18(2), pp 163, 2007) and discuss a connection between polyconvexity and the Grötzsch free boundary value problem. Special cases of our results can also be obtained from earlier works by Astala et al. (Elliptic partial differential equations and quasiconformal mappings in the plane, Princeton University Press, Princeton, 2008) and Yan (Trans Am Math Soc 355(12):4755–4765, 2003). Since the restricted domain of the energy functions in question poses additional difficulties with respect to the notion of quasiconvexity compared to the case of globally defined real-valued functions, we also discuss more general properties related to the $$W^{1,p}$$ W 1 , p -quasiconvex envelope on the domain $${{\,\mathrm{GL}\,}}^{\!+}(n)$$ GL + ( n ) which, in particular, ensure that a stricter version of Dacorogna’s formula is applicable to conformally invariant energies on $${{\,\mathrm{GL}\,}}^{\!+}(2)$$ GL + ( 2 ) .


Author(s):  
Philippe D’Iribarne ◽  
Sylvie Chevrier ◽  
Alain Henry ◽  
Jean-Pierre Segal ◽  
Geneviève Tréguer-Felten

We are experiencing a rather curious situation today. Globalization is in full swing. International cooperation actions are more and more frequent. An increasing number of agents, who were socialized in different worlds, experience first-hand the difficulties that need to be overcome in such situations. Yet management practices are being homogenized all over the world. The elites in emerging countries are falling over themselves to follow the expensive training given by Western universities. Attempts to achieve a global standardization of management practices have probably never been stretched so far in multinational companies. However, the dissemination of the best practices of a management claiming to be universal is confronted with the irreducible resistance of the diversity of cultures. This resistance remains poorly understood. The most common representation of cultural differences taught in universities and in training seminars for companies disregards the analysis of concrete realities, thus failing to shed light on what is actually taking place in these encounters. Understanding this constitutes a major intellectual and practical challenge for researchers who focus on both ...


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