An iterative contractive framework for probe methods: LASSO

We present a new iterative approach called Line Adaptation for the Singular Sources Objective (LASSO) to object or shape reconstruction based on the singular sources method (or probe method) for the reconstruction of scatterers from the far-field pattern of scattered acoustic or electromagnetic waves. The scheme is based on the construction of an indicator function given by the scattered field for incident point sources in its source point from the given far-field patterns for plane waves. The indicator function is then used to drive the contraction of a surface which surrounds the unknown scatterers. A stopping criterion for those parts of the surfaces that touch the unknown scatterers is formulated. A splitting approach for the contracting surfaces is formulated, such that scatterers consisting of several separate components can be reconstructed. Convergence of the scheme is shown, and its feasibility is demonstrated using a numerical study with several examples.

Centrality and spectral radius in dynamic communication networks

We explore the influence of the choice of attenuation factor on Katz centrality indices for evolving communication networks. For given snapshots of a network observed over a period of time, recently developed communicability indices aim to identify best broadcasters and listeners in the network. In this article, we looked into the sensitivity of communicability indices on the attenuation factor constraint, in relation to spectral radius (the largest eigenvalue) of the network at any point in time and its computation in the case of large networks. We proposed relaxed communicability measures where the spectral radius bound on attenuation factor is relaxed and the adjacency matrix is normalised in order to maintain the convergence of the measure. Using a vitality based measure of both standard and relaxed communicability indices we looked at the ways of establishing the most important individuals for broadcasting and receiving of messages related to community bridging roles. We illustrated our findings with two examples of real-life networks, MIT reality mining data set of daily communications between 106 individuals during one year and UK Twitter mentions network, direct messages on Twitter between 12.4k individuals during one week.

Sharing power? Prospects for a U.S. concert-balance strategy

The Pax Americana and the grand strategy of hegemony (or “Primacy”) that underpins it may be becoming unsustainable. Particularly in the wake of exhausting wars, the Global Financial Crisis, and the shift of wealth from West to East, it may no longer be possible or prudent for the United States to act as the unipolar sheriff or guardian of a world order. But how viable are the alternatives, and what difficulties will these alternatives entail in their design and execution? This analysis offers a sympathetic but critical analysis of alternative U.S. National Security Strategies of “retrenchment” that critics of American diplomacy offer. In these strategies, the United States would anticipate the coming of a more multipolar world and organize its behavior around the dual principles of “concert” and “balance,” seeking a collaborative relationship with other great powers, while being prepared to counterbalance any hostile aggressor that threatens world order. The proponents of such strategies argue that by scaling back its global military presence and its commitments, the United States can trade prestige for security, shift burdens, and attain a more free hand. To support this theory, they often look to the 19th-century concert of Europe as a model of a successful security regime and to general theories about the natural balancing behavior of states. This monograph examines this precedent and measures its usefulness for contemporary statecraft to identify how great power concerts are sustained and how they break down. The project also applies competing theories to how states might behave if world politics are in transition: Will they balance, bandwagon, or hedge? This demonstrates the multiple possible futures that could shape and be shaped by a new strategy. viii A new strategy based on an acceptance of multipolarity and the limits of power is prudent. There is scope for such a shift. The convergence of several trends—including transnational problems needing collaborative efforts, the military advantages of defenders, the reluctance of states to engage in unbridled competition, and hegemony fatigue among the American people—means that an opportunity exists internationally and at home for a shift to a new strategy. But a Concert-Balance strategy will still need to deal with several potential dilemmas. These include the difficulty of reconciling competitive balancing with cooperative concerts, the limits of balancing without a forward-reaching onshore military capability, possible unanticipated consequences such as a rise in regional power competition or the emergence of blocs (such as a Chinese East Asia or an Iranian Gulf), and the challenge of sustaining domestic political support for a strategy that voluntarily abdicates world leadership. These difficulties can be mitigated, but they must be met with pragmatic and gradual implementation as well as elegant theorizing and the need to avoid swapping one ironclad, doctrinaire grand strategy for another.

On asymptotic behavior at infinity and the finite section method for integral equations on the half-line

e consider integral equations on the half-line of the form and the finite section approximation to x obtained by replacing the infinite limit of integration by the finite limit β. We establish conditions under which, if the finite section method is stable for the original integral equation (i.e. exists and is uniformly bounded in the space of bounded continuous functions for all sufficiently large β), then it is stable also for a perturbed equation in which the kernel k is replaced by k + h. The class of perturbations allowed includes all compact and some non-compact perturbations of the integral operator. Using this result we study the stability and convergence of the finite section method in the space of continuous functions x for which ()()()=−∫∞dttxt,sk)s(x0()syβxβx()sxsp+1 is bounded. With the additional assumption that ()(tskt,sk−≤ where ()()(),qsomefor,sassOskandRLkq11>+∞→=∈− we show that the finite-section method is stable in the weighted space for ,qp≤≤0 provided it is stable on the space of bounded continuous functions. With these results we establish error bounds in weighted spaces for x - xβ and precise information on the asymptotic behaviour at infinity of x. We consider in particular the case when the integral operator is a perturbation of a Wiener-Hopf operator and illustrate this case with a Wiener-Hopf integral equation arising in acoustics.