C-diagrams, shifts and solidarity values

In the theory of cooperative games so called dividends of a coalition $S$ are considered, which are defined as $\frac{c_S}{|S|}$. The costs $c_S$ form a c-diagram. On these c-diagrams several types of shifts are defined and analysed. Different solution concepts and their properties are related to shifts. We introduce reward games and fine games as components of a cooperative game. Some solution concepts for applications are analysed in terms of c-diagrams, as well as the solidarity concept. \u

An approximation algorithm for a facility location problem with stochastic demands

In this article we propose, for any $\epsilon>0$, a $2(1+\epsilon)$-approximation algorithm for a facility location problem with stochastic demands. This problem can be described as follows. There are a number of locations, where facilities may be opened and a number of demand points, where requests for items arise at random. The requests are sent to open facilities. At the open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. After constant times, the inventory is replenished to a fixed order up to level. The time interval between consecutive replenishments is called a reorder period. The problem is where to locate the facilities and how to assign the demand points to facilities at minimal cost per reorder period such that the above mentioned quality of service is insured. The incurred costs are the expected transportation costs from the demand points to the facilities, the operating costs (opening costs) of the facilities and the investment in inventory (inventory costs). \u

A simple dual ascent algorithm for the multilevel facility location problem

We present a simple dual ascent method for the multilevel facility location problem which finds a solution within $6$ times the optimum for the uncapacitated case and within $12$ times the optimum for the capacitated one. The algorithm is deterministic and based on the primal-dual technique. \u

A combinatorial approximation algorithm for CDMA downlink rate allocation

This paper presents a combinatorial algorithm for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalue of that matrix, which provides a quick assessment of the feasibility of the power assignment for a given downlink rate allocation. Based on the Perron-Frobenius eigenvalue, we reduce the downlink rate allocation problem to a set of multiple-choice knapsack problems. The solution of these problems provides an approximation of the optimal downlink rate allocation and cell borders for which the system throughput, expressed in terms of utility functions of the users, is maximized

World trends in fertilizer use and projections to 2020

Fertilizers have played an important role in increased crop production, especially in cereal yields, and will continue to be a cornerstone of the science-based agriculture required to feed the expanding world population. Fertilizers replenish the nutrients removed from soils by harvested crops, encourage adoption of high-yielding varieties, and increase biomass in the nutrient-poor soils of the tropics. Bumb and Baanante trace fertilizer use until the 1990s as well as production and price trends. Finally they propose projected trends in use, requirements, and production. The authors conclude that, overall, a conducive and stable policy environment, including macroeconomic stability, price incentives, credit availability, efficient organizational arrangements, research and extension support, regulatory frameworks, and environmental monitoring, will be essential to promote environmentally friendly growth in fertilizer use and supply to 2020.Fertilizers. ,Crops Economic aspects. ,Cereal crops. ,Environmental protection. ,

Adaptive Learning Technique For Facial Recognition

This research describes the adaptive learning technique for facial recognition. It is a common practice in convolutional neural network(CNN) based facial recognition to save its trained result on a large dataset and then load and apply it to ongoing facial recognition tasks. This generally used method lacks adaptation, and the ongoing evolution of new knowledge poses a key technical challenge. In this research, we propose a continued learning technique to incorporate new knowledge derived in each facial recognition process. A positive recognition with confidence score is assigned, and the image associated with this confidence is added to the image dataset for ongoing training. Pre-trained CNN on a similar small dataset serves as the starting point for this ongoing training technique, which leads to a significant reduction in the training time and enhancement of the recognition rate. This research is inspired by the evolutionary adaptive learning talk given by Dr. Harry Li in the 2019 SiliconValley AI Event. This research is conducted to provide proof-of-concept groundwork to demonstrate the feasibility of continued learning and adaptation while executing the FaceNet/ResNet facial recognition algorithm. In this research, the proof-of-the-concept algorithm is demonstrated on a simple feed-forward neural network, then tested with an adaptive face technique to demonstrate the learning acceleration from the adaptive process. Experiments confirm the adaptive learning on FaceNet and ResNet as per the proof-of-the-concept by reducing the number of epochs required to reach a convergence point by approximately 50%. This states the use of adaptive learning techniques in software that require identifying images of aging people concerning time

The standard set game of a cooperative game

We show that for every cooperative game a corresponding set game can be defined, called the standard set game. Values for set games can be applied to this standard game and determine allocations for the cooperative game. On the other hand, notions for cooperative games, like the Shapley value, the $\tau-$value or the core can be considered in the context of the standard set games. \u

Approximation algorithms for facility location problems

Facility location problems are among the most well-studied problems in optimization literature. The simplest variant is the uncapacitated facility location problem, which we denoted by the UFLP. In the UFLP, we are given a set of possible facility locations and a set of clients. The problem seeks to find a set of locations to build/open facilities such that the sum of the cost of building/opening the facilities and the cost of serving each client from exactly one open facility is minimized. This problem is NP−hard. Therefore, many heuristics for finding good approximate solutions were developed. In this thesis we design approximation algorithms for several variants of the UFLP

Global spatial regularity for a regularized elasto-plastic model

In this note the spatial regularity of weak solutions for a class of elasto-viscoplastic evolution models is studied for nonsmooth domains. The considered class comprises e.g. models which are obtained through a Yosida regularization from classical, rate-independent models. The corresponding evolution model consists of an elliptic PDE for the (generalized) displacements which is coupled with an ordinary differential equation with a Lipschitz continuous nonlinearity describing the evolution of the internal variable. It is shown that the global spatial regularity of the displacements and the inner variables is exactly determined through the mapping properties of the underlying elliptic operator