In this paper we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We introduce the concept of fair capital allocations and provide explicit…
In this paper, we combine the design of band-pass frequency selective surfaces (FSSs) with polarization converters to realize a broadband frequency-selective polarization converter (FSPC) with lowbackward scattering, which consists of the top polarization conversion layer backed by a multi-layer bandpass FSS. It is numerically demonstrated that the 1 dB transmission window can be obtained from…
Energetic neutral atoms (ENA) are an important tool for investigating the structure of the heliosphere. Recently, it was observed that fluxes of ENAs (with energy $\le$ 55 keV) coming from the upwind and downwind regions of the heliosphere are similar in strength. This led the authors of these observations to hypothesize that the heliosphere is…
This paper reexamines the validity of the natural resource curse hypothesis, using the database of mineral exporting countries. Our findings are as follows: (i) Resource-rich countries (RRCs) do not necessarily exhibit poor political, economic and social performance; (ii) RRCs that perform poorly have a low diversified exports portfolio; (iii) In contrast, RRCs with a low…
We consider the facility location problem in the one-dimensional setting where each facility can serve a limited number of agents from the algorithmic and mechanism design perspectives. From the algorithmic perspective, we prove that the corresponding optimization problem, where the goal is to locate facilities to minimize either the total cost to all agents or…
Vehicle-to-everything (V2X) communication in the mmWave band is one way to achieve high data-rates for applications like infotainment, cooperative perception, and augmented reality assisted driving etc. MmWave communication relies on large antennas arrays, and configuring these arrays poses high training overhead. In this article, we motivate the use of infrastructure mounted sensors (which will be…
In this work, we are going to find sufficient conditions on the initial triaxial Bianchi IX metric on some 4-dimensional manifolds foliated by homogeneous S3 for a Type I singularity to occur when it is flowed under the Ricci flow. This work generalises the study on rotationally symmetric manifolds done by Angenent and Isenberg as…
For a graph $G$, let $\chi (G)$ denote the chromatic number. In graph theory, the following famous conjecture posed by Hedetniemi has been studied: For two graphs $G$ and $H$, $\chi (G\times H)=\min\{\chi (G),\chi (H)\}$, where $G \times H$ is the tensor product of $G$ and $H$. In this paper, we give a reduction of…
Throughout modern society, human users interact with large-scale engineered systems, e.g., road-traffic networks, electric power grids, wireless communication networks. As the performance of such systems greatly depends on the decisions made by the individual users – often leading to undesirable system behaviour – a natural question arises: How can we design incentives to promote efficient…
The discrete KdV (dKdV) equation, the pinnacle of discrete integrability, is often thought to possess the singularity confinement property because it confines on an elementary quadrilateral. Here we investigate the singularity structure of the dKdV equation through reductions of the equation, obtained for initial conditions on a staircase with height 1, and show that it…