The Experts below are selected from a list of 7992 Experts worldwide ranked by ideXlab platform
Arul Mishra - One of the best experts on this subject based on the ideXlab platform.
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thinking outside the euclidean box riemannian geometry and inter temporal decision making
PLOS ONE, 2016Co-Authors: Himanshu Mishra, Arul MishraAbstract:Inter-temporal decisions involves assigning values to various payoffs occurring at different temporal distances. Past research has used different approaches to study these decisions made by humans and animals. For instance, considering that people discount future payoffs at a Constant rate (e.g., exponential discounting) or at variable rate (e.g., hyperbolic discounting). In this research, we question the widely assumed, but seldom questioned, notion across many of the existing approaches that the decision space, where the decision-maker perceives time and monetary payoffs, is a Euclidean space. By relaxing the rigid assumption of Euclidean space, we propose that the decision space is a more flexible Riemannian space of Constant Negative Curvature. We test our proposal by deriving a discount function, which uses the distance in the Negative Curvature space instead of Euclidean temporal distance. The distance function includes both perceived values of time as well as money, unlike past work which has considered just time. By doing so we are able to explain many of the empirical findings in inter-temporal decision-making literature. We provide converging evidence for our proposal by estimating the Curvature of the decision space utilizing manifold learning algorithm and showing that the characteristics (i.e., metric properties) of the decision space resembles those of the Negative Curvature space rather than the Euclidean space. We conclude by presenting new theoretical predictions derived from our proposal and implications for how non-normative behavior is defined.
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thinking outside the euclidean box riemannian geometry and inter temporal decision making
2015Co-Authors: Himanshu Mishra, Arul MishraAbstract:Inter-temporal decisions involves assigning values to various payoffs occurring at different temporal distances. Past research has used different approaches to study these decisions made by humans and animals. For instance, considering that people discount future payoffs at a Constant rate (e.g., exponential discounting) or at variable rate (e.g., hyperbolic discounting). In this research, we question the widely assumed, but seldom questioned, notion across many of the existing approaches that the decision space, where the decision-maker perceives time and payoffs, is a Euclidean space. By relaxing the rigid assumption of Euclidean space, we propose that the decision space is a more flexible Riemannian space of Constant Negative Curvature. We test our proposal by deriving a discount function, which uses the distance in the Negative Curvature space instead of Euclidean temporal distance. The distance function includes both perceived values of time as well as money, unlike past work which has considered just time. By doing so we are able to explain many of the empirical findings in inter-temporal decision-making literature. We provide converging evidence for our proposal by estimating the Curvature of the decision space utilizing manifold learning algorithm and showing that the characteristics (i.e., metric properties) of the decision space resembles those of the Negative Curvature space rather than the Euclidean space. We conclude by presenting new theoretical predictions derived from our proposal and implications for how non-normative behavior is defined.
Himanshu Mishra - One of the best experts on this subject based on the ideXlab platform.
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thinking outside the euclidean box riemannian geometry and inter temporal decision making
PLOS ONE, 2016Co-Authors: Himanshu Mishra, Arul MishraAbstract:Inter-temporal decisions involves assigning values to various payoffs occurring at different temporal distances. Past research has used different approaches to study these decisions made by humans and animals. For instance, considering that people discount future payoffs at a Constant rate (e.g., exponential discounting) or at variable rate (e.g., hyperbolic discounting). In this research, we question the widely assumed, but seldom questioned, notion across many of the existing approaches that the decision space, where the decision-maker perceives time and monetary payoffs, is a Euclidean space. By relaxing the rigid assumption of Euclidean space, we propose that the decision space is a more flexible Riemannian space of Constant Negative Curvature. We test our proposal by deriving a discount function, which uses the distance in the Negative Curvature space instead of Euclidean temporal distance. The distance function includes both perceived values of time as well as money, unlike past work which has considered just time. By doing so we are able to explain many of the empirical findings in inter-temporal decision-making literature. We provide converging evidence for our proposal by estimating the Curvature of the decision space utilizing manifold learning algorithm and showing that the characteristics (i.e., metric properties) of the decision space resembles those of the Negative Curvature space rather than the Euclidean space. We conclude by presenting new theoretical predictions derived from our proposal and implications for how non-normative behavior is defined.
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thinking outside the euclidean box riemannian geometry and inter temporal decision making
2015Co-Authors: Himanshu Mishra, Arul MishraAbstract:Inter-temporal decisions involves assigning values to various payoffs occurring at different temporal distances. Past research has used different approaches to study these decisions made by humans and animals. For instance, considering that people discount future payoffs at a Constant rate (e.g., exponential discounting) or at variable rate (e.g., hyperbolic discounting). In this research, we question the widely assumed, but seldom questioned, notion across many of the existing approaches that the decision space, where the decision-maker perceives time and payoffs, is a Euclidean space. By relaxing the rigid assumption of Euclidean space, we propose that the decision space is a more flexible Riemannian space of Constant Negative Curvature. We test our proposal by deriving a discount function, which uses the distance in the Negative Curvature space instead of Euclidean temporal distance. The distance function includes both perceived values of time as well as money, unlike past work which has considered just time. By doing so we are able to explain many of the empirical findings in inter-temporal decision-making literature. We provide converging evidence for our proposal by estimating the Curvature of the decision space utilizing manifold learning algorithm and showing that the characteristics (i.e., metric properties) of the decision space resembles those of the Negative Curvature space rather than the Euclidean space. We conclude by presenting new theoretical predictions derived from our proposal and implications for how non-normative behavior is defined.
Alicia J Kollar - One of the best experts on this subject based on the ideXlab platform.
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hyperbolic lattices in circuit quantum electrodynamics
Nature, 2019Co-Authors: Alicia J Kollar, Mattias Fitzpatrick, Andrew HouckAbstract:After two decades of development, cavity quantum electrodynamics with superconducting circuits has emerged as a rich platform for quantum computation and simulation. Lattices of coplanar waveguide resonators constitute artificial materials for microwave photons, in which interactions between photons can be incorporateded either through the use of nonlinear resonator materials or through coupling between qubits and resonators. Here we make use of the previously overlooked property that these lattice sites are deformable and permit tight-binding lattices that are unattainable even in solid-state systems. We show that networks of coplanar waveguide resonators can create a class of materials that constitute lattices in an effective hyperbolic space with Constant Negative Curvature. We present numerical simulations of hyperbolic analogues of the kagome lattice that show unusual densities of states in which a macroscopic number of degenerate eigenstates comprise a spectrally isolated flat band. We present a proof-of-principle experimental realization of one such lattice. This paper represents a step towards on-chip quantum simulation of materials science and interacting particles in curved space.
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hyperbolic lattices in circuit quantum electrodynamics
arXiv: Quantum Physics, 2018Co-Authors: Alicia J Kollar, Mattias Fitzpatrick, Andrew HouckAbstract:After close to two decades of research and development, superconducting circuits have emerged as a rich platform for both quantum computation and quantum simulation. Lattices of superconducting coplanar waveguide (CPW) resonators have been shown to produce artificial materials for microwave photons, where weak interactions can be introduced either via non-linear resonator materials or strong interactions via qubit-resonator coupling. Here, we introduce a technique using networks of CPW resonators to create a new class of materials which constitute regular lattices in an effective hyperbolic space with Constant Negative Curvature. We show numerical simulations of a class of hyperbolic analogs of the kagome lattice which show unusual densities of states with a spectrally-isolated degenerate flat band. We also present an experimental realization of one of these lattices, exhibiting the aforementioned band structure. This paper represents the first step towards on-chip quantum simulation of materials science and interacting particles in curved space.
Simeon Polshin - One of the best experts on this subject based on the ideXlab platform.
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quantization of massless fields over the static robertson walker space of Constant Negative Curvature
Classical and Quantum Gravity, 2001Co-Authors: Simeon PolshinAbstract:Taking the 1×H3 space as an example, we develop the new method of quantization of fields over symmetric spaces. We construct the quantized massless fields of an arbitrary spin over the 1×H3 space by the resolution over the systems of `plane waves', which are solutions of the corresponding wave equations. The propagators of these fields are 1×SO(3,1)-invariant and causal. For spin-0 and spin-½ fields the propagators are obtained in an explicit form.
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quantization of massless fields over the static robertson walker space of Constant Negative Curvature
arXiv: General Relativity and Quantum Cosmology, 2000Co-Authors: Simeon PolshinAbstract:Taking the ${\Bbb R}^1 \times H^3$ space as an example, we develop the new method of quantization of fields over symmetric spaces. We construct the quantized massless fields of an arbitrary spin over the ${\Bbb R}^1 \times H^3$ space by the resolution over the systems of "plane waves" which are solutions of the corresponding wave equations. The propagators of these fields are ${\Bbb R}^1 \times SO(3,1)$-invariant and causal. For spin 0 and 1/2 fields the propagators are obtained in the explicit form.
A A Saharian - One of the best experts on this subject based on the ideXlab platform.
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wightman function and the casimir effect for a robin sphere in a Constant Curvature space
European Physical Journal C, 2014Co-Authors: S Bellucci, A A Saharian, N A SaharyanAbstract:We evaluate the Wightman function, the mean field squared and the vacuum expectation value of the energy–momentum tensor for a scalar field with the Robin boundary condition on a spherical shell in the background of a Constant Negative Curvature space. For the coefficient in the boundary condition there is a critical value above which the scalar vacuum becomes unstable. In both the interior and the exterior regions, the vacuum expectation values are decomposed into the boundary-free and sphere-induced contributions. For the latter, rapidly convergent integral representations are provided. In the region inside the sphere, the eigenvalues are expressed in terms of the zeros of the combination of the associated Legendre function and its derivative and the decomposition is achieved by making use of the Abel–Plana type summation formula for the series over these zeros. The sphere-induced contribution to the vacuum expectation value of the field squared is Negative for the Dirichlet boundary condition and positive for the Neumann one. At distances from the sphere larger than the Curvature scale of the background space the suppression of the vacuum fluctuations in the gravitational field corresponding to the Negative Curvature space is stronger compared with the case of the Minkowskian bulk. In particular, the decay of the vacuum expectation values with the distance is exponential for both massive and massless fields. The corresponding results are generalized for spaces with spherical bubbles and for cosmological models with Negative Curvature spaces.
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A summation formula over the zeros of the associated Legendre function with a physical application
Journal of Physics A: Mathematical and Theoretical, 2008Co-Authors: A A SaharianAbstract:Associated Legendre functions arise in many problems of mathematical physics. By using the generalized Abel–Plana formula, in this paper we derive a summation formula for the series over the zeros of the associated Legendre function of the first kind with respect to the degree. The summation formula for the series over the zeros of the Bessel function, previously discussed in the literature, is obtained as a limiting case. The Wightman function for a scalar field with a general Curvature coupling parameter is considered inside a spherical boundary on the background of a Constant Negative Curvature space. The corresponding mode sum contains the series over the zeros of the associated Legendre function. The application of the summation formula allows us to present the Wightman function in the form of the sum of two integrals. The first one corresponds to the Wightman function for the bulk geometry without boundaries and the second one is induced by the presence of the spherical shell. For points away from the boundary the latter is finite in the coincidence limit. In this way the renormalization of the vacuum expectation value of the field squared is reduced to that for the boundary-free part.
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summation formula over the zeros of the associated legendre function with a physical application
arXiv: Mathematical Physics, 2008Co-Authors: A A SaharianAbstract:Associated Legendre functions arise in many problems of mathematical physics. By using the generalized Abel-Plana formula, in this paper we derive a summation formula for the series over the zeros of the associated Legendre function of the first kind with respect to the degree. The summation formula for the series over the zeros of the Bessel function, previously discussed in the literature, is obtained as a limiting case. The Wightman function for a scalar field with general Curvature coupling parameter is considered inside a spherical boundary on background of Constant Negative Curvature space. The corresponding mode sum contains series over the zeros of the associated Legendre function. The application of the summation formula allows us to present the Wightman function in the form of the sum of two integrals. The first one corresponds to the Wightman function for the bulk geometry without boundaries and the second one is induced by the presence of the spherical shell. For points away from the boundary the latter is finite in the coincidence limit. In this way the renormalization of the vacuum expectation value of the field squared is reduced to that for the boundary-free part.