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M J Reboucas - One of the best experts on this subject based on the ideXlab platform.
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probing spatial Orientability of friedmann robertson walker spatially flat spacetime
arXiv: General Relativity and Quantum Cosmology, 2021Co-Authors: Nivaldo A Lemos, Daniel Muller, M J ReboucasAbstract:One important global topological property of a spacetime manifold is Orientability. It is widely believed that spatial Orientability can only be tested by global journeys around the Universe to check for orientation-reversing closed paths. Since such global journeys are not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. The nonexistence of globally defined spinor fields on a non-orientable spacetime is another theoretical argument for Orientability. However, it is conceivable that Orientability can be put to test by local physical effects. In this paper, we show that it is possible to locally access spatial Orientability of a spatially flat Friedmann--Robertson-Walker spacetime through quantum vacuum electromagnestic fluctuations. We argue that a putative non-Orientability of the spatial sections of spatially flat FRW spacetime can be ascertained by the study of the stochastic motions of a charged particle or a point electric dipole under quantum vacuum electromagnetic fluctuations. In particular, the stochastic motions of a dipole permit the recognition of a presumed non-Orientability of $3-$space in itself.
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inquiring electromagnetic quantum fluctuations about the Orientability of space
European Physical Journal C, 2021Co-Authors: Nivaldo A Lemos, M J ReboucasAbstract:Orientability is an important global topological property of spacetime manifolds. It is often assumed that a test for spatial Orientability requires a global journey across the whole 3-space to check for orientation-reversing paths. Since such a global expedition is not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. Another theoretical argument also offered to support this choice comes from the impossibility of having globally defined spinor fields on non-orientable spacetime manifolds. In this paper, we argue that it is possible to locally access spatial Orientability of Minkowski empty spacetime through physical effects involving quantum vacuum electromagnetic fluctuations. We study the motions of a charged particle and a point electric dipole subject to these electromagnetic fluctuations in Minkowski spacetime with orientable and non-orientable spatial topologies. We derive analytic expressions for a statistical Orientability indicator for both of these point-like particles in two inequivalent spatially flat topologies. For the charged particle, we show that it is possible to distinguish the orientable from the non-orientable topology by contrasting the time evolution of the Orientability indicators. This result reveals that it is possible to access Orientability through electromagnetic quantum vacuum fluctuations. However, the answer to the central question of the paper, namely how to locally probe the Orientability of Minkowski 3-space intrinsically, comes about only in the study of the motions of an electric dipole. For this point-like particle, we find that a characteristic inversion pattern exhibited by the curves of the Orientability statistical indicator is a signature of non-Orientability. This result makes it clear that it is possible to locally unveil spatial non-Orientability through the inversion pattern of curves of our Orientability indicator for a point electric dipole under quantum vacuum electromagnetic fluctuations. Our findings might open the way to a conceivable experiment involving quantum vacuum electromagnetic fluctuations to locally probe the spatial Orientability of Minkowski empty spacetime.
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inquiring electromagnetic quantum fluctuations about the Orientability of space
arXiv: High Energy Physics - Theory, 2020Co-Authors: Nivaldo A Lemos, M J ReboucasAbstract:Orientability is an important topological property of spacetime manifolds. It is generally assumed that a test for spatial Orientability requires a journey across the whole 3-space to check for orientation-reversing paths. Since such a global expedition is not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are offered to support the choosing of time- and space-orientable spacetime manifolds. We show that it is possible to access spatial Orientability of Minkowski spacetime through local physical effects involving quantum electromagnetic fluctuations. To this end, we study the motions of a charged particle and an electric dipole under these fluctuations in Minkowski spacetime with orientable and non-orientable spatial topologies. We derive expressions for an Orientability indicator for both point-like particles in two spatially flat topologies. For the particle, we show that it is possible to distinguish the orientable from the non-orientable topology by contrasting the evolution of the indicators. This shows that it is possible to access Orientability through electromagnetic quantum fluctuations.The answer to the question on how to locally probe the Orientability of Minkowski 3-space intrinsically arises in the study of the dipole's motions. We find that a characteristic inversion pattern exhibited by the dipole indicator curves is a signature of non-Orientability. This result makes it clear that it is possible to locally unveil spatial non-Orientability by the inversion pattern of Orientability indicator curves of an electric dipole under electromagnetic fluctuations. Our findings open the way to a conceivable experiment involving quantum electromagnetic fluctuations to locally probe the spatial Orientability on the microscopic scale of Minkowski spacetime.
Nivaldo A Lemos - One of the best experts on this subject based on the ideXlab platform.
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probing spatial Orientability of friedmann robertson walker spatially flat spacetime
arXiv: General Relativity and Quantum Cosmology, 2021Co-Authors: Nivaldo A Lemos, Daniel Muller, M J ReboucasAbstract:One important global topological property of a spacetime manifold is Orientability. It is widely believed that spatial Orientability can only be tested by global journeys around the Universe to check for orientation-reversing closed paths. Since such global journeys are not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. The nonexistence of globally defined spinor fields on a non-orientable spacetime is another theoretical argument for Orientability. However, it is conceivable that Orientability can be put to test by local physical effects. In this paper, we show that it is possible to locally access spatial Orientability of a spatially flat Friedmann--Robertson-Walker spacetime through quantum vacuum electromagnestic fluctuations. We argue that a putative non-Orientability of the spatial sections of spatially flat FRW spacetime can be ascertained by the study of the stochastic motions of a charged particle or a point electric dipole under quantum vacuum electromagnetic fluctuations. In particular, the stochastic motions of a dipole permit the recognition of a presumed non-Orientability of $3-$space in itself.
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inquiring electromagnetic quantum fluctuations about the Orientability of space
European Physical Journal C, 2021Co-Authors: Nivaldo A Lemos, M J ReboucasAbstract:Orientability is an important global topological property of spacetime manifolds. It is often assumed that a test for spatial Orientability requires a global journey across the whole 3-space to check for orientation-reversing paths. Since such a global expedition is not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are usually offered to support the choosing of time- and space-orientable spacetime manifolds. Another theoretical argument also offered to support this choice comes from the impossibility of having globally defined spinor fields on non-orientable spacetime manifolds. In this paper, we argue that it is possible to locally access spatial Orientability of Minkowski empty spacetime through physical effects involving quantum vacuum electromagnetic fluctuations. We study the motions of a charged particle and a point electric dipole subject to these electromagnetic fluctuations in Minkowski spacetime with orientable and non-orientable spatial topologies. We derive analytic expressions for a statistical Orientability indicator for both of these point-like particles in two inequivalent spatially flat topologies. For the charged particle, we show that it is possible to distinguish the orientable from the non-orientable topology by contrasting the time evolution of the Orientability indicators. This result reveals that it is possible to access Orientability through electromagnetic quantum vacuum fluctuations. However, the answer to the central question of the paper, namely how to locally probe the Orientability of Minkowski 3-space intrinsically, comes about only in the study of the motions of an electric dipole. For this point-like particle, we find that a characteristic inversion pattern exhibited by the curves of the Orientability statistical indicator is a signature of non-Orientability. This result makes it clear that it is possible to locally unveil spatial non-Orientability through the inversion pattern of curves of our Orientability indicator for a point electric dipole under quantum vacuum electromagnetic fluctuations. Our findings might open the way to a conceivable experiment involving quantum vacuum electromagnetic fluctuations to locally probe the spatial Orientability of Minkowski empty spacetime.
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inquiring electromagnetic quantum fluctuations about the Orientability of space
arXiv: High Energy Physics - Theory, 2020Co-Authors: Nivaldo A Lemos, M J ReboucasAbstract:Orientability is an important topological property of spacetime manifolds. It is generally assumed that a test for spatial Orientability requires a journey across the whole 3-space to check for orientation-reversing paths. Since such a global expedition is not feasible, theoretical arguments that combine universality of physical experiments with local arrow of time, CP violation and CPT invariance are offered to support the choosing of time- and space-orientable spacetime manifolds. We show that it is possible to access spatial Orientability of Minkowski spacetime through local physical effects involving quantum electromagnetic fluctuations. To this end, we study the motions of a charged particle and an electric dipole under these fluctuations in Minkowski spacetime with orientable and non-orientable spatial topologies. We derive expressions for an Orientability indicator for both point-like particles in two spatially flat topologies. For the particle, we show that it is possible to distinguish the orientable from the non-orientable topology by contrasting the evolution of the indicators. This shows that it is possible to access Orientability through electromagnetic quantum fluctuations.The answer to the question on how to locally probe the Orientability of Minkowski 3-space intrinsically arises in the study of the dipole's motions. We find that a characteristic inversion pattern exhibited by the dipole indicator curves is a signature of non-Orientability. This result makes it clear that it is possible to locally unveil spatial non-Orientability by the inversion pattern of Orientability indicator curves of an electric dipole under electromagnetic fluctuations. Our findings open the way to a conceivable experiment involving quantum electromagnetic fluctuations to locally probe the spatial Orientability on the microscopic scale of Minkowski spacetime.
Stefan Walzer - One of the best experts on this subject based on the ideXlab platform.
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peeling close to the Orientability threshold spatial coupling in hashing based data structures
Symposium on Discrete Algorithms, 2021Co-Authors: Stefan WalzerAbstract:In multiple-choice data structures each element $x$ in a set $S$ of $m$ keys is associated with a random set $e(x) \subseteq [n]$ of buckets with capacity $\ell \geq 1$ by hash functions. This setting is captured by the hypergraph $H = ([n],\{e(x) \mid x \in S\})$. Accomodating each key in an associated bucket amounts to finding an $\ell$-orientation of $H$ assigning to each hyperedge an incident vertex such that each vertex is assigned at most $\ell$ hyperedges. If each subhypergraph of $H$ has minimum degree at most $\ell$, then an $\ell$-orientation can be found greedily and $H$ is called $\ell$-peelable. Peelability has a central role in invertible Bloom lookup tables and can speed up the construction of retrieval data structures, perfect hash functions and cuckoo hash tables. Many hypergraphs exhibit sharp density thresholds with respect to $\ell$-Orientability and $\ell$-peelability, i.e. as the density $c = \frac{m}{n}$ grows past a critical value, the probability of these properties drops from almost $1$ to almost $0$. In fully random $k$-uniform hypergraphs the thresholds $c_{k,\ell}^*$ for $\ell$-Orientability significantly exceed the thresholds for $\ell$-peelability. In this paper, for every $k \geq 2$ and $\ell \geq 1$ with $(k,\ell) \neq (2,1)$ and every $z > 0$, we construct a new family of random $k$-uniform hypergraphs with i.i.d. random hyperedges such that both the $\ell$-peelability and the $\ell$-Orientability thresholds approach $c_{k,\ell}^*$ as $z \rightarrow \infty$. We exploit the phenomenon of threshold saturation via spatial coupling discovered in the context of low-density parity-check codes. Once the connection to data structures is in plain sight, a framework by Kudekar, Richardson and Urbanke (2015) does the heavy lifting in our proof.
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peeling close to the Orientability threshold spatial coupling in hashing based data structures
arXiv: Data Structures and Algorithms, 2020Co-Authors: Stefan WalzerAbstract:Hypergraphs with random hyperedges underlie various data structures where hash functions map inputs to hyperedges, e.g. cuckoo hash tables, invertible Bloom lookup tables, retrieval data structures and perfect hash functions. High memory efficiency and quick query times call for high hyperedge density and small hyperedge size. Moreover, Orientability or even peelability of the hypergraph is required or advantageous. For $k$-uniform fully random hypergraphs, the thresholds $c_{k,\ell}^*$ for $\ell$-Orientability significantly exceed the thresholds for $\ell$-peelability. In this paper, for every $k \geq 2$ and $\ell \geq 1$ with $(k,\ell) \neq (2,1)$ and every $z > 0$, we construct a new family of random $k$-uniform hypergraphs with i.i.d. random hyperedges such that both the $\ell$-peelability and the $\ell$-Orientability thresholds approach $c_{k,\ell}^*$ as $z \rightarrow \infty$. Our construction is simple: The $N$ vertices are linearly ordered and each hyperedge selects its $k$ elements uniformly at random from a random range of $\frac{N}{z}$ consecutive vertices. We thus exploit the phenomenon of threshold saturation via spatial coupling discovered in the context of low density parity check codes. Once the connection to data structures is in plain sight, we employ a framework by Kudekar, Richardson and Urbanke (2015) to do the heavy lifting in our proof. We demonstrate the usefulness of our construction, using our hypergraphs as a drop-in replacement in a retrieval data structure by Botelho et al. (2013). This reduces memory usage from $1.23m$ bits to $1.12m$ bits (for input size $m$) with no downsides.
Naichung Conan Leung - One of the best experts on this subject based on the ideXlab platform.
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Orientability for gauge theories on calabi yau manifolds
Advances in Mathematics, 2017Co-Authors: Yalong Cao, Naichung Conan LeungAbstract:Abstract We study Orientability issues of moduli spaces from gauge theories on Calabi–Yau manifolds. Our results generalize and strengthen those for Donaldson–Thomas theory on Calabi–Yau manifolds of dimensions 3 and 4. We also prove a corresponding result in the relative situation which is relevant to the gluing formula in DT theory.
Lazar Kopanja - One of the best experts on this subject based on the ideXlab platform.
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on the Orientability of shapes
IEEE Transactions on Image Processing, 2006Co-Authors: Jovisa žunic, Paul L Rosin, Lazar KopanjaAbstract:The orientation of a shape is a useful quantity, and has been shown to affect performance of object recognition in the human visual system. Shape orientation has also been used in computer vision to provide a properly oriented frame of reference, which can aid recognition. However, for certain shapes, the standard moment-based method of orientation estimation fails. We introduce as a new shape feature shape Orientability, which defines the degree to which a shape has distinct (but not necessarily unique) orientation. A new method is described for measuring shape Orientability, and has several desirable properties. In particular, unlike the standard moment-based measure of elongation, it is able to differentiate between the varying levels of Orientability of n-fold rotationally symmetric shapes. Moreover, the new Orientability measure is simple and efficient to compute (for an n-gon we describe an O(n) algorithm)
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shape Orientability
Asian Conference on Computer Vision, 2006Co-Authors: Jovisa žunic, Paul L Rosin, Lazar KopanjaAbstract:In this paper we consider some questions related to the orientation of shapes. We introduce as a new shape feature shape Orientability, i.e. the degree to which a shape has distinct (but not necessarily unique) orientation. A new method is described for measuring shape Orientability, and has several desirable properties. In particular, unlike the standard moment based measure of elongation, it is able to differentiate between the varying levels of Orientability of n-fold rotationally symmetric shapes.