136 research outputs found
A system-theoretic framework for privacy preservation in continuous-time multiagent dynamics
In multiagent dynamical systems, privacy protection corresponds to avoid
disclosing the initial states of the agents while accomplishing a distributed
task. The system-theoretic framework described in this paper for this scope,
denoted dynamical privacy, relies on introducing output maps which act as
masks, rendering the internal states of an agent indiscernible by the other
agents as well as by external agents monitoring all communications. Our output
masks are local (i.e., decided independently by each agent), time-varying
functions asymptotically converging to the true states. The resulting masked
system is also time-varying, and has the original unmasked system as its limit
system. When the unmasked system has a globally exponentially stable
equilibrium point, it is shown in the paper that the masked system has the same
point as a global attractor. It is also shown that existence of equilibrium
points in the masked system is not compatible with dynamical privacy.
Application of dynamical privacy to popular examples of multiagent dynamics,
such as models of social opinions, average consensus and synchronization, is
investigated in detail.Comment: 38 pages, 4 figures, extended version of arXiv preprint
arXiv:1808.0808
The geometric phase of stock trading
Geometric phases describe how in a continuous-time dynamical system the
displacement of a variable (called phase variable) can be related to other
variables (shape variables) undergoing a cyclic motion, according to an area
rule. The aim of this paper is to show that geometric phases can exist also for
discrete-time systems, and even when the cycles in shape space have zero area.
A context in which this principle can be applied is stock trading. A zero-area
cycle in shape space represents the type of trading operations normally carried
out by high-frequency traders (entering and exiting a position on a fast
time-scale), while the phase variable represents the cash balance of a trader.
Under the assumption that trading impacts stock prices, even zero-area cyclic
trading operations can induce geometric phases, i.e., profits or losses,
without affecting the stock quote.Comment: 15 pages, 12 figure
Representing multiqubit unitary evolutions: spin coherences and infinitesimal coherences
For the tensor of coherences parametrization of a multiqubit density
operator, we provide an explicit formulation of the corresponding unitary
dynamics at infinitesimal level. The main advantage of this formalism (clearly
reminiscent of the idea of ``coherences'' and ``coupling Hamiltonians'' of spin
systems) is that the pattern of correlation between qubits and the pattern of
infinitesimal correlation are highlighted simultaneously and can be used
constructively for qubit manipulation. For example, it allows to compute
explicitly a Rodrigues' formula for the one-parameter orbits of nonlocal
Hamiltonians. The result is easily generalizable to orbits of Cartan
subalgebras and allows to write the Cartan decomposition of unitary propagators
as a linear action.Comment: significantly rewritten, 9 pages, 4 figure
A dynamical approach to privacy preserving average consensus
In this paper we propose a novel method for achieving average consensus in a
continuous-time multiagent network while avoiding to disclose the initial
states of the individual agents. In order to achieve privacy protection of the
state variables, we introduce maps, called output masks, which alter the value
of the states before transmitting them. These output masks are local (i.e.,
implemented independently by each agent), deterministic, time-varying and
converging asymptotically to the true state. The resulting masked system is
also time-varying and has the original (unmasked) system as its limit system.
It is shown in the paper that the masked system has the original average
consensus value as a global attractor. However, in order to preserve privacy,
it cannot share an equilibrium point with the unmasked system, meaning that in
the masked system the global attractor cannot be also stable.Comment: 19 pages, 2 figures (minor changes w.r.t. previous version
Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control
In this paper we investigate parametrization-free solutions of the problem of
quantum pure state preparation and subspace stabilization by means of
Hamiltonian control, continuous measurement and quantum feedback, in the
presence of a Markovian environment. In particular, we show that whenever
suitable dissipative effects are induced either by the unmonitored environment
or by non Hermitian measurements, there is no need for feedback control to
accomplish the task. Constructive necessary and sufficient conditions on the
form of the open-loop controller can be provided in this case. When open-loop
control is not sufficient, filtering-based feedback control laws steering the
evolution towards a target pure state are provided, which generalize those
available in the literature
Dynamics over Signed Networks
A signed network is a network with each link associated with a positive or
negative sign. Models for nodes interacting over such signed networks, where
two different types of interactions take place along the positive and negative
links, respectively, arise from various biological, social, political, and
economic systems. As modifications to the conventional DeGroot dynamics for
positive links, two basic types of negative interactions along negative links,
namely the opposing rule and the repelling rule, have been proposed and studied
in the literature. This paper reviews a few fundamental convergence results for
such dynamics over deterministic or random signed networks under a unified
algebraic-graphical method. We show that a systematic tool of studying node
state evolution over signed networks can be obtained utilizing generalized
Perron-Frobenius theory, graph theory, and elementary algebraic recursions.Comment: In press, SIAM Revie
Signed bounded confidence models for opinion dynamics
The aim of this paper is to modify continuous-time bounded confidence opinion dynamics models so
that ‘‘changes of opinion’’ (intended as changes of the sign of the initial states) are never induced during
the evolution. Such sign invariance can be achieved by letting opinions of different sign localized near the
origin interact negatively, or neglect each other, or even repel each other. In all cases, it is possible to obtain
sign-preserving bounded confidence models with state-dependent connectivity and with a clustering
behavior similar to that of a standard bounded confidence model
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