General solutions to $$\mathcal {N}$$-field cosmology with exponential potentials

We construct the general analytical solution for the $$\mathcal {N}$$ N -field product-exponential potential in an expanding FLRW background. We demonstrate the relevance of this analytical solution in more general contexts for the derivation of estimates for the transitional time between an arbitrary initial state and the slow-roll solutions. In certain cases, these estimates can also be used to demonstrate the non-linear convergence towards the slow-roll solutions. In addition, we extend the solution to include stiff matter as well.

PDα-type iterative learning control with initial state learning for fractional-order systems

In order to eliminate the influence of the arbitrary initial state on the systems, open-loop and open-close-loop PDα-type fractional-order iterative learning control (FOILC) algorithms with initial state learning are proposed for a class of fractional-order linear continuous-time systems with an arbitrary initial state. In the sense of Lebesgue-p norm, the sufficient conditions for the convergence of PDα-type algorithms are disturbed in the iteration domain by taking advantage of the generalized Young inequality of convolution integral. The results demonstrate that under these novel algorithms, the convergences of the tracking error are can be guaranteed. Numerical simulations support the effectiveness and correctness of the proposed algorithms.

Network Controllability Analysis of Three Multiple-myeloma Patient Genetic Mutation Datasets

Network controllability focuses on the concept of driving the dynamical system associated to a directed network of interactions from an arbitrary initial state to an arbitrary final state, through a well-chosen set of input functions applied in a minimal number of so-called input nodes. In earlier studies we and other groups demonstrated the potential of applying this concept in medicine. A directed network of interactions may be built around the main known drivers of the disease being studied, and then analysed to identify combinations of drug targets controlling survivability-essential genes in the network. This paper takes the next step and focuses on patient data. We demonstrate that comprehensive protein-protein interaction networks can be built around patient genetic data, and that network controllability can be used to identify possible personalised drug combinations. We discuss the algorithmic methods that can be used to construct and analyse these networks.

Network Controllability Analysis of Three Multiple-myeloma Patient Genetic Mutation Datasets

Network controllability focuses on the concept of driving the dynamical system associated to a directed network of interactions from an arbitrary initial state to an arbitrary final state, through a well-chosen set of input functions applied in a minimal number of so-called input nodes. In earlier studies we and other groups demonstrated the potential of applying this concept in medicine. A directed network of interactions may be built around the main known drivers of the disease being studied, and then analysed to identify combinations of drug targets controlling survivability-essential genes in the network. This paper takes the next step and focuses on patient data. We demonstrate that comprehensive protein-protein interaction networks can be built around patient genetic data, and that network controllability can be used to identify possible personalised drug combinations. We discuss the algorithmic methods that can be used to construct and analyse these networks.

Recursive Solution of Queue Length Distribution for Geo/G/1 Queue with Delayed Min(N, D)-Policy

In this paper we consider a discrete-time Geo/G/1 queue with delayed Min(N, D)-policy. Using renewal process theory, total probability decomposition technique and z-transform, we study the transient and equilibrium properties of the queue length from an arbitrary initial state, and obtain both the recursive expressions of the transient state queue length distribution and the steady state queue length distribution at arbitrary time epoch n+. Furthermore, we derive the important relations between equilibrium queue length distributions at different time epochs n–, n and n+. Finally, we give some numerical examples about capacity decision in queueing systems to demonstrate the application of the analytical results reported in this paper.

Implicit Coordination Using FOND Planning

Epistemic planning can be used to achieve implicit coordination in cooperative multi-agent settings where knowledge and capabilities are distributed between the agents. In these scenarios, agents plan and act on their own without having to agree on a common plan or protocol beforehand. However, epistemic planning is undecidable in general. In this paper, we show how implicit coordination can be achieved in a simpler, propositional setting by using nondeterminism as a means to allow the agents to take the other agents' perspectives. We identify a decidable fragment of epistemic planning that allows for arbitrary initial state uncertainty and non-determinism, but where actions can never increase the uncertainty of the agents. We show that in this fragment, planning for implicit coordination can be reduced to a version of fully observable nondeterministic (FOND) planning and that it thus has the same computational complexity as FOND planning. We provide a small case study, modeling the problem of multi-agent path finding with destination uncertainty in FOND, to show that our approach can be successfully applied in practice.

Heat-Bath Algorithmic Cooling with optimal thermalization strategies

Heat-Bath Algorithmic Cooling is a set of techniques for producing highly pure quantum systems by utilizing a surrounding heat-bath and unitary interactions. These techniques originally used the thermal environment only to fully thermalize ancillas at the environment temperature. Here we extend HBAC protocols by optimizing over the thermalization strategy. We find, for any d-dimensional system in an arbitrary initial state, provably optimal cooling protocols with surprisingly simple structure and exponential convergence to the ground state. Compared to the standard ones, these schemes can use fewer or no ancillas and exploit memory effects to enhance cooling. We verify that the optimal protocols are robusts to various deviations from the ideal scenario. For a single target qubit, the optimal protocol can be well approximated with a Jaynes-Cummings interaction between the system and a single thermal bosonic mode for a wide range of environmental temperatures. This admits an experimental implementation close to the setup of a micromaser, with a performance competitive with leading proposals in the literature. The proposed protocol provides an experimental setup that illustrates how non-Markovianity can be harnessed to improve cooling. On the technical side we 1. introduce a new class of states called maximallyactivestates and discuss their thermodynamic significance in terms of optimal unitary control, 2. introduce a new set of thermodynamic processes, called β-permutations, whose access is sufficient to simulate a generic thermalization process, 3. show how to use abstract toolbox developed within the resource theory approach to thermodynamics to perform challenging optimizations, while combining it with open quantum system dynamics tools to approximate optimal solutions within physically realistic setups.

Generic Quantum Markov Semigroups with Degenerate Ground States: The Fock Case

We consider quantum Markov semigroups arising from the weak coupling limit of a system with generic Hamiltonian coupled to a boson Fock zero temperature reservoir. We find all the invariant states of a generic quantum Markov semigroup and compute explicitly the limit invariant state explicitly starting from an arbitrary initial state. We also show that convergence is exponentially fast under some natural assumptions.

Emergent Properties and Connectionism

This chapter analyzes connectionism. In this alternative orientation in cognitive science, the brain has once more become the main source of metaphors and ideas. Theories and models no longer begin with abstract symbolic descriptions but with a whole army of neural-like, simple, unintelligent components, which, when appropriately connected, have interesting global properties. These global properties embody and express the cognitive capacities being sought. The entire approach depends, then, on introducing the appropriate connections, which is usually done through a rule for the gradual change of connections starting from a fairly arbitrary initial state. One of the important factors contributing to the explosive interest in this approach today was the introduction of some effective methods of following the changes that can occur in these networks. Indeed, great attention has been given to the introduction of statistical measures that provide the system with a global energy function that permits one to follow how the system arrives into convergent states.