The Experts below are selected from a list of 32523 Experts worldwide ranked by ideXlab platform
Andrés Bujosa - One of the best experts on this subject based on the ideXlab platform.
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FoIKS - Implementing Term Algebra Syntactic Unification in Free Modules over Certain Rings
Lecture Notes in Computer Science, 2002Co-Authors: Robin N. Banerjee, Andrés BujosaAbstract:We have shown elsewhere how to introduce a concept of syntactic unification when terms are taken as the elements in a Free Module. This is done so as to obtain an m.g.u and its uniqueness modulo isomorphism. Here we introduce the concept of an implementation: An injective function from a term algebra into another object in a different category, both Free over the same denumerable set of variables, but which carries over a generalised form of the so called Unification Axiom. We show that any implementation induces a faithful representation of the semigroup of substitutions of a term algebra in an appropriately chosen semigroup of homomorphisms in the target structure. We moreover show that this representation assigns unifiers to unifiers and, under certain conditions, an m.g.u. to an m.g.u. Moreover, when the target structure for an implementation is another term algebra, we show that a unification problem is solvable in the target if and only if it is so in the original term algebra. We qualify these implementations as faithful. However, when the target structure is a Free Module of the type mentioned, we show by means of a counter-example that there exist non-faithful implementations. We then give a necessary and sufficient condition for an implementation on one of these Modules to be faithful. Strikingly, this condition is nothing but a translation into the language of the Module of the well-known occurs-check property of usual syntactic unification. Finally we construct an example of a faithful implementation of a term algebra in one of our Free Modules.
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Syntactic Unification as a Geometric Operation in Free Modules over certain Rings
Electronic Notes in Theoretical Computer Science, 2002Co-Authors: Robin N. Banerjee, Andrés BujosaAbstract:Abstract We have shown elsewhere how to introduce a concept of syntactic unification when terms are taken as the elements in a Free Module and established the link between both unification concepts showing that, under certain reasonable hypotheses, they are completely equivalent. Here we show how syntactic unification of terms may be viewed as the intersection of certain subsets in a Free Module, which strongly resemble affine varieties in vector spaces. Thus this work represents a first step in the way towards a purely geometric interpretation of logic programming.
Robin N. Banerjee - One of the best experts on this subject based on the ideXlab platform.
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FoIKS - Implementing Term Algebra Syntactic Unification in Free Modules over Certain Rings
Lecture Notes in Computer Science, 2002Co-Authors: Robin N. Banerjee, Andrés BujosaAbstract:We have shown elsewhere how to introduce a concept of syntactic unification when terms are taken as the elements in a Free Module. This is done so as to obtain an m.g.u and its uniqueness modulo isomorphism. Here we introduce the concept of an implementation: An injective function from a term algebra into another object in a different category, both Free over the same denumerable set of variables, but which carries over a generalised form of the so called Unification Axiom. We show that any implementation induces a faithful representation of the semigroup of substitutions of a term algebra in an appropriately chosen semigroup of homomorphisms in the target structure. We moreover show that this representation assigns unifiers to unifiers and, under certain conditions, an m.g.u. to an m.g.u. Moreover, when the target structure for an implementation is another term algebra, we show that a unification problem is solvable in the target if and only if it is so in the original term algebra. We qualify these implementations as faithful. However, when the target structure is a Free Module of the type mentioned, we show by means of a counter-example that there exist non-faithful implementations. We then give a necessary and sufficient condition for an implementation on one of these Modules to be faithful. Strikingly, this condition is nothing but a translation into the language of the Module of the well-known occurs-check property of usual syntactic unification. Finally we construct an example of a faithful implementation of a term algebra in one of our Free Modules.
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Syntactic Unification as a Geometric Operation in Free Modules over certain Rings
Electronic Notes in Theoretical Computer Science, 2002Co-Authors: Robin N. Banerjee, Andrés BujosaAbstract:Abstract We have shown elsewhere how to introduce a concept of syntactic unification when terms are taken as the elements in a Free Module and established the link between both unification concepts showing that, under certain reasonable hypotheses, they are completely equivalent. Here we show how syntactic unification of terms may be viewed as the intersection of certain subsets in a Free Module, which strongly resemble affine varieties in vector spaces. Thus this work represents a first step in the way towards a purely geometric interpretation of logic programming.
Alessandro Zampa - One of the best experts on this subject based on the ideXlab platform.
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A[Sl_q(2)] at roots of unity is a Free Module over A[Sl(2)]
arXiv: Quantum Algebra, 2000Co-Authors: Ludwik Dabrowski, Cesare Reina, Alessandro ZampaAbstract:It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SL_q(2)) is a Free Module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided.
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A(SLq(2)) at Roots of Unity is a Free Module over A(SL(2))
Letters in Mathematical Physics, 2000Co-Authors: Ludwik Dabrowski, Cesare Reina, Alessandro ZampaAbstract:It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SLq(2)) is a Free Module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided.
Ludwik Dabrowski - One of the best experts on this subject based on the ideXlab platform.
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A[Sl_q(2)] at roots of unity is a Free Module over A[Sl(2)]
arXiv: Quantum Algebra, 2000Co-Authors: Ludwik Dabrowski, Cesare Reina, Alessandro ZampaAbstract:It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SL_q(2)) is a Free Module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided.
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A(SLq(2)) at Roots of Unity is a Free Module over A(SL(2))
Letters in Mathematical Physics, 2000Co-Authors: Ludwik Dabrowski, Cesare Reina, Alessandro ZampaAbstract:It is shown that when q is a primitive root of unity of order not equal to 2 mod 4, A(SLq(2)) is a Free Module of finite rank over the coordinate ring of the classical group SL(2). An explicit set of generators is provided.
Marios Savvides - One of the best experts on this subject based on the ideXlab platform.
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feature selective anchor Free Module for single shot object detection
Computer Vision and Pattern Recognition, 2019Co-Authors: Chenchen Zhu, Marios SavvidesAbstract:We motivate and present feature selective anchor-Free (FSAF) Module, a simple and effective building block for single-shot object detectors. It can be plugged into single-shot detectors with feature pyramid structure. The FSAF Module addresses two limitations brought up by the conventional anchor-based detection: 1) heuristic-guided feature selection; 2) overlap-based anchor sampling. The general concept of the FSAF Module is online feature selection applied to the training of multi-level anchor-Free branches. Specifically, an anchor-Free branch is attached to each level of the feature pyramid, allowing box encoding and decoding in the anchor-Free manner at an arbitrary level. During training, we dynamically assign each instance to the most suitable feature level. At the time of inference, the FSAF Module can work independently or jointly with anchor-based branches. We instantiate this concept with simple implementations of anchor-Free branches and online feature selection strategy. Experimental results on the COCO detection track show that our FSAF Module performs better than anchor-based counterparts while being faster. When working jointly with anchor-based branches, the FSAF Module robustly improves the baseline RetinaNet by a large margin under various settings, while introducing nearly Free inference overhead. And the resulting best model can achieve a state-of-the-art 44.6% mAP, outperforming all existing single-shot detectors on COCO.
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feature selective anchor Free Module for single shot object detection
arXiv: Computer Vision and Pattern Recognition, 2019Co-Authors: Chenchen Zhu, Marios SavvidesAbstract:We motivate and present feature selective anchor-Free (FSAF) Module, a simple and effective building block for single-shot object detectors. It can be plugged into single-shot detectors with feature pyramid structure. The FSAF Module addresses two limitations brought up by the conventional anchor-based detection: 1) heuristic-guided feature selection; 2) overlap-based anchor sampling. The general concept of the FSAF Module is online feature selection applied to the training of multi-level anchor-Free branches. Specifically, an anchor-Free branch is attached to each level of the feature pyramid, allowing box encoding and decoding in the anchor-Free manner at an arbitrary level. During training, we dynamically assign each instance to the most suitable feature level. At the time of inference, the FSAF Module can work jointly with anchor-based branches by outputting predictions in parallel. We instantiate this concept with simple implementations of anchor-Free branches and online feature selection strategy. Experimental results on the COCO detection track show that our FSAF Module performs better than anchor-based counterparts while being faster. When working jointly with anchor-based branches, the FSAF Module robustly improves the baseline RetinaNet by a large margin under various settings, while introducing nearly Free inference overhead. And the resulting best model can achieve a state-of-the-art 44.6% mAP, outperforming all existing single-shot detectors on COCO.
