1,698 research outputs found
A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations
We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the
dependence of the coefficients is nonlinear and nonlocal in time with respect
to the unknowns. We extend the numerical scheme proposed and studied recently
by the authors for a single FPK equation of this type. We analyse the
convergence of the scheme and we study its applicability in two examples. The
first one concerns a population model involving two interacting species and the
second one concerns two populations Mean Field Games
Time machines: the Principle of Self-Consistency as a consequence of the Principle of Minimal Action
We consider the action principle to derive the classical, non-relativistic
motion of a self-interacting particle in a 4-D Lorentzian spacetime containing
a wormhole and which allows the existence of closed time-like curves. For the
case of a `hard-sphere' self-interaction potential we show that the only
possible trajectories (for a particle with fixed initial and final positions
and which traverses the wormhole once) minimizing the classical action are
those which are globally self-consistent, and that the `Principle of
self-consistency' (originally introduced by Novikov) is thus a natural
consequence of the `Principle of minimal action.'Comment: 26 pages, plain latex; modified version includes extra constraint for
collinear collision case and other minor misprints correction
Time-optimal CNOT between indirectly coupled qubits in a linear Ising chain
We give analytical solutions for the time-optimal synthesis of entangling
gates between indirectly coupled qubits 1 and 3 in a linear spin chain of three
qubits subject to an Ising Hamiltonian interaction with equal coupling plus
a local magnetic field acting on the intermediate qubit. The energy available
is fixed, but we relax the standard assumption of instantaneous unitary
operations acting on single qubits. The time required for performing an
entangling gate which is equivalent, modulo local unitary operations, to the
between the indirectly coupled qubits 1 and 3 is
, i.e. faster than a previous estimate based on a similar
Hamiltonian and the assumption of local unitaries with zero time cost.
Furthermore, performing a simple Walsh-Hadamard rotation in the Hlibert space
of qubit 3 shows that the time-optimal synthesis of the (which acts as the identity when the control qubit 1 is in the state
, while if the control qubit is in the state the target
qubit 3 is flipped as ) also requires the same
time .Comment: 9 pages; minor modification
Time Optimal Unitary Operations
Extending our previous work on time optimal quantum state evolution, we
formulate a variational principle for the time optimal unitary operation, which
has direct relevance to quantum computation. We demonstrate our method with
three examples, i.e. the swap of qubits, the quantum Fourier transform and the
entangler gate, by choosing a two-qubit anisotropic Heisenberg model.Comment: 4 pages, 1 figure. References adde
Cosmology as Relativistic Particle Mechanics: From Big Crunch to Big Bang
Cosmology can be viewed as geodesic motion in an appropriate metric on an
`augmented' target space; here we obtain these geodesics from an effective
relativistic particle action. As an application, we find some exact (flat and
curved) cosmologies for models with N scalar fields taking values in a
hyperbolic target space for which the augmented target space is a Milne
universe. The singularities of these cosmologies correspond to points at which
the particle trajectory crosses the Milne horizon, suggesting a novel
resolution of them, which we explore via the Wheeler-deWitt equation.Comment: 17 pages, 3 figures, references and comments adde
Dynamical Generation of Spacetime Signature by Massive Quantum Fields on a Topologically Non-Trivial Background
The effective potential for a dynamical Wick field (dynamical signature)
induced by the quantum effects of massive fields on a topologically non-trivial
dimensional background is considered. It is shown that when the radius of
the compactified dimension is very small compared with (where
is a proper-time cutoff), a flat metric with Lorentzian signature is
preferred on . When the compactification radius
becomes larger a careful analysis of the 1-loop effective potential indicates
that a Lorentzian signature is preferred in both and and that these
results are relatively stable under metrical perturbations
Decentralized Federated Learning and Network Topologies: An Empirical Study on Convergence
Federated Learning is a well-known learning paradigm that allows the distributed training of machine learning models. Federated Learning keeps data in the source devices and communicates only the model's coefficients to a centralized server. This paper studies the decentralized flavor of Federated Learning. A peer-to-peer network replaces the centralized server, and nodes exchange model's coefficients directly. In particular, we look for empirical evidence on the effect of different network topologies and communication parameters on the convergence in the training of distributed models. Our observations suggest that small-world networks converge faster for small amounts of nodes, while xx are more suitable for larger setups
Energy and QoE aware Placement of Applications and Data at the Edge
Recent years are witnessing extensions of cyber-infrastructures towards distributed environments. The Edge of the network is gaining a central role in the agenda of both infrastructure and application providers. Following the actual distributed structure of such a computational environment, nowadays, many solutions face resource and application management needs in Cloud/Edge continua. One of the most challenging aspects is ensuring highly available computing and data infrastructures while optimizing the system's energy consumption. In this paper, we describe a decentralized solution that limits the energy consumption by the system without failing to match the users' expectations, defined as the services' Quality of Experience (QoE) when accessing data and leveraging applications at the Edge. Experimental evaluations through simulation conducted with PureEdgeSim demonstrate the effectiveness of the approach
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