4,069 research outputs found
Scale-free interpersonal influences on opinions in complex systems
An important side effect of the evolution of the human brain is an increased
capacity to form opinions in a very large domain of issues, which become points
of aggressive interpersonal disputes. Remarkably, such disputes are often no
less vigorous on small differences of opinion than large differences. Opinion
differences that may be measured on the real number line may not directly
correspond to the subjective importance of an issue and extent of resistance to
opinion change. This is a hard problem for field of opinion dynamics, a field
that has become increasingly prominent as it has attracted more contributions
to it from investigators in the natural and engineering sciences. The paper
contributes a scale-free approach to assessing the extents to which
individuals, with unknown heterogeneous resistances to influence, have been
influenced by the opinions of others
Complex Objects in the Polytopes of the Linear State-Space Process
A simple object (one point in -dimensional space) is the resultant of the
evolving matrix polynomial of walks in the irreducible aperiodic network
structure of the first order DeGroot (weighted averaging) state-space process.
This paper draws on a second order generalization the DeGroot model that allows
complex object resultants, i.e, multiple points with distinct coordinates, in
the convex hull of the initial state-space. It is shown that, holding network
structure constant, a unique solution exists for the particular initial space
that is a sufficient condition for the convergence of the process to a
specified complex object. In addition, it is shown that, holding network
structure constant, a solution exists for dampening values sufficient for the
convergence of the process to a specified complex object. These dampening
values, which modify the values of the walks in the network, control the
system's outcomes, and any strongly connected typology is a sufficient
condition of such control
Two Steps to Obfuscation
This note addresses the historical antecedents of the 1998 PageRank measure
of centrality. An identity relation links it to 1990-1991 models of Friedkin
and Johnsen
Monetary policy with model uncertainty: distribution forecast targeting
We examine optimal and other monetary policies in a linear-quadratic setup with a relatively general form of model uncertainty, so-called Markov jump-linear-quadratic systems extended to include forward-looking variables. The form of model uncertainty our framework encompasses includes : simple i.i.d. model deviations; serially correlated model deviations; estimable regimeswitching models; more complex structural uncertainty about very different models, for instance, backward- and forward-looking models; time-varying central-bank judgment about the state of model uncertainty; and so forth. We provide an algorithm for finding the optimal policy as well as solutions for arbitrary policy functions. This allows us to compute and plot consistent distribution forecasts "fan charts" of target variables and instruments. Our methods hence extend certainty equivalence and "mean forecast targeting" to more general certainty non-equivalence and "distribution forecast targeting." --Optimal policy,multiplicative uncertainty
Energy-constrained two-way assisted private and quantum capacities of quantum channels
With the rapid growth of quantum technologies, knowing the fundamental
characteristics of quantum systems and protocols is essential for their
effective implementation. A particular communication setting that has received
increased focus is related to quantum key distribution and distributed quantum
computation. In this setting, a quantum channel connects a sender to a
receiver, and their goal is to distill either a secret key or entanglement,
along with the help of arbitrary local operations and classical communication
(LOCC). In this work, we establish a general theory of energy-constrained,
LOCC-assisted private and quantum capacities of quantum channels, which are the
maximum rates at which an LOCC-assisted quantum channel can reliably establish
secret key or entanglement, respectively, subject to an energy constraint on
the channel input states. We prove that the energy-constrained squashed
entanglement of a channel is an upper bound on these capacities. We also
explicitly prove that a thermal state maximizes a relaxation of the squashed
entanglement of all phase-insensitive, single-mode input bosonic Gaussian
channels, generalizing results from prior work. After doing so, we prove that a
variation of the method introduced in [Goodenough et al., New J. Phys. 18,
063005 (2016)] leads to improved upper bounds on the energy-constrained
secret-key-agreement capacity of a bosonic thermal channel. We then consider a
multipartite setting and prove that two known multipartite generalizations of
the squashed entanglement are in fact equal. We finally show that the
energy-constrained, multipartite squashed entanglement plays a role in bounding
the energy-constrained LOCC-assisted private and quantum capacity regions of
quantum broadcast channels.Comment: 31 pages, 6 figure
Novel Multidimensional Models of Opinion Dynamics in Social Networks
Unlike many complex networks studied in the literature, social networks
rarely exhibit unanimous behavior, or consensus. This requires a development of
mathematical models that are sufficiently simple to be examined and capture, at
the same time, the complex behavior of real social groups, where opinions and
actions related to them may form clusters of different size. One such model,
proposed by Friedkin and Johnsen, extends the idea of conventional consensus
algorithm (also referred to as the iterative opinion pooling) to take into
account the actors' prejudices, caused by some exogenous factors and leading to
disagreement in the final opinions.
In this paper, we offer a novel multidimensional extension, describing the
evolution of the agents' opinions on several topics. Unlike the existing
models, these topics are interdependent, and hence the opinions being formed on
these topics are also mutually dependent. We rigorous examine stability
properties of the proposed model, in particular, convergence of the agents'
opinions. Although our model assumes synchronous communication among the
agents, we show that the same final opinions may be reached "on average" via
asynchronous gossip-based protocols.Comment: Accepted by IEEE Transaction on Automatic Control (to be published in
May 2017
Quantifying the Impact of Option-Based Compensation on Earnings for the 50 Largest U.S. Technology Companies
- …