In this paper we study a facility location problem in the plane in which a single point (facility) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time from the clients to the facility, using the L1 or Manhattan metric. The rapid transit line is given by a segment with any length and orientation, and is an alternative transportation line that ...

1 In this paper we study a facility location problem in the plane in which a single point (facility) 2 and a rapid transit line (highway) are simultaneously located in order to minimize the total travel 3 time of the clients to the facility, using the L1 or Manhattan metric. The rapid transit line is 4 represented by a line segment with fixed length and arbitrary orientation. The highway is an ...

Many image denoising methods can be characterized as minimizing “loss + penalty,” where the “loss” measures the fidelity of the denoised image to the data, and the “penalty” measures the smoothness of the denoising function. In this paper, we propose two models that use the L1-norm of the pixel updates as the penalty. The L1-norm penalty has the advantage of changing only the noisy pixels, whil...

Let n respondents rank order d items, and suppose that . Our main task is to uncover display the structure of observed data by an exploratory riffle shuffling procedure which sequentially decomposes voters into a finite number coherent groups plus a noisy group: where group represents outlier each group composed finite number clusters. We consider exploratory riffle set of items to be equ...

The l1/l2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the l1/l2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of ...

2. Surveys comparing the quality of taxi services across countries are quite common. In France, every year, the “hotels.com” taxi survey makes the headlines of the newspapers when it comes out. Its press release () specifies: “Research was conducted amongst 1,400 travellers from the UK, Ireland, France, Spain, Germany, Norway, Sweden and Denmark in May 2009.” In its last three issues London’s c...

Two kinds of optimal convergence orders in L1-norm to a self-similar solution are proved or conjectured for various evolutionary problems so far. The first convergence order is of the magnitude of the similarity solution itself and the second one is of order 1/t . Employing a potential comparison technique to scalar conservation laws we may easily see that these asymptotic convergence orders ar...