Abstract:
Reverse pricing has been recognized as an effective tool to handle the uncertainty of users' demands in the travel industry (e.g., airlines and hotels). To investigate its viability in cellular networks, we study the practical limitations of (operator-driven) time-dependent pricing that has been recently introduced, taking into account demand uncertainty. Then, we endeavor to design the reverse pricing mechanism to resolve the weakness of the time-dependent pricing scheme. We show that the proposed pricing scheme can achieve "triple-win" solutions: an increase in the total revenue of the operator; higher resource utilization efficiency; and an increment in the total payoff of the users. Our findings provide a new outlook on resource management, and design guidelines for adopting the reverse pricing scheme.

Abstract:
A significant challenge in bacterial detection is the identification of viable bacteria over debris, specifically post decontamination. Of increasing concern are antibiotic resistant strains that require accurate and rapid post decontamination analysis. Current strategies are fraught with disadvantages and most of them are not selective for viable bacteria. However, bacteria are critically dependent upon iron sequestration, synthesizing and releasing siderophores (SDPs) to tightly bind iron, with the subsequent uptake of iron bound SDPs. This is a highly conserved process that occurs only in intact bacteria. Herein we report a facile method to use bacterial SDPs to selectively and rapidly identify only viable bacteria in complex matrices, and discriminate them from their dead counterparts. Desferrioxamine B (Desf B) tethered to a glass slide is used to specifically capture viable bacteria from a mixture of viable and dead Escherichia coli, as demonstrated by fluorescence microscopy. We re- port both direct conjugation of Desf B on thin-film-coated glass slides as well as biotin-streptavidin conjugation strategies, both of which are successful in the said goal. We have analyzed the density of images obtained upon fluorescence staining using edge detection with a Canny edge detector. This novel application of a software analysis tool originally developed for satellite imaging to biological staining allows for accurate quantitation of observed data.

Abstract:
Scatter processes of photons lead to blurring of images produced by CT (computed tomography) or CBCT (cone beam computed tomography) in the KV domain or portal imaging in the MV domain (KV: kilovolt age, MV: megavoltage). Multiple scatter is described by, at least, one Gaussian kernel. In various situations, this approximation is crude, and we need two/three Gaussian kernels to account for the long-range tails (Landau tails), which appear in the Moli\`ere scatter of protons, energy straggling and electron capture of charged particles passing through matter and Compton scatter of photons. The ideal image (source function) is subjected to Gaussian convolutions to yield a blurred image recorded by a detector array. The inverse problem is to obtain the ideal source image from measured image. Deconvolution methods of linear combinations of two/three Gaussian kernels with different parameters s0, s1, s2 can be derived via an inhomogeneous Fredholm integral equation of second kind (IFIE2) and Liouville - Neumann series (LNS) to provide the source function {\rho}. The determination of scatter parameter functions s0, s1, s2 can be best determined by Monte-Carlo simulations. A particular advantage of this procedure is given, if the scatter functions s0, s1, s2 are not constant and depend on coordinates. This fact implies that the scatter functions can be calibrated according to the electron density {\rho}electron provided by image reconstructions. The convergence criterion of LNS can always be satisfied with regard to the above mentioned cases. A generalization of the present theory is given by an analysis of convolution problems based on the Dirac equation and Fermi-Dirac statistics leading to Landau tails. This generalization is applied to Bethe-Bloch equation (BBE) of charged particles to analyze electron capture. The methodology can readily be extended to other disciplines of physics.

Abstract:
We address a linear control system under geometric constraints on control and study its reachable sets starting at zero time from the origin. The main result is the existence of a limit shape of the reachable sets as the terminal time tends to zero. Here, a shape of a set stands for the set regarded up to an invertible linear transformation. Both autonomous and non-autonomous cases are considered.

Abstract:
We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage early-stage distributions from propagation schemes such as random walks to capture structural information encoded in node labels, attributes, and edge information. This has two benefits. First, off-the-shelf propagation schemes can be used to naturally construct kernels for many graph types, including labeled, partially labeled, unlabeled, directed, and attributed graphs. Second, by leveraging existing efficient and informative propagation schemes, propagation kernels can be considerably faster than state-of-the-art approaches without sacrificing predictive performance. We will also show that if the graphs at hand have a regular structure, for instance when modeling image or video data, one can exploit this regularity to scale the kernel computation to large databases of graphs with thousands of nodes. We support our contributions by exhaustive experiments on a number of real-world graphs from a variety of application domains.

Abstract:
We present a necessary and sufficient condition for the reachable set, i.e., the set of states reachable from a ball of initial states at some time, of an ordinary differential equation to be convex. In particular, convexity is guaranteed if the ball of initial states is sufficiently small, and we provide an upper bound on the radius of that ball, which can be directly obtained from the right hand side of the differential equation. In finite dimensions, our results cover the case of ellipsoids of initial states. A potential application of our results is inner and outer polyhedral approximation of reachable sets, which becomes extremely simple and almost universally applicable if these sets are known to be convex. We demonstrate by means of an example that the balls of initial states for which the latter property follows from our results are large enough to be used in actual computations.

Abstract:
We are interested in the determination of the reachable states for the boundary control of the one-dimensional heat equation. We consider either one or two boundary controls. We show that reachable states associated with square integrable controls can be extended to analytic functions onsome square of C, and conversely, that analytic functions defined on a certain disk can be reached by using boundary controlsthat are Gevrey functions of order 2. The method of proof combines the flatness approach with some new Borel interpolation theorem in some Gevrey class witha specified value of the loss in the uniform estimates of the successive derivatives of the interpolating function.

Abstract:
In this paper, we propose a reachable set based collision avoidance algorithm for unmanned aerial vehicles (UAVs). UAVs have been deployed for agriculture research and management, surveillance and sensor coverage for threat detection and disaster search and rescue operations. It is essential for the aircraft to have on-board collision avoidance capability to guarantee safety. Instead of the traditional approach of collision avoidance between trajectories, we propose a collision avoidance scheme based on reachable sets and tubes. We then formulate the problem as a convex optimization problem seeking suitable control constraint sets for participating aircraft. We have applied the approach on a case study of two quadrotors collision avoidance scenario.

Abstract:
Motivation: Models of discrete concurrent systems often lead to huge and complex state transition graphs that represent their dynamics. This makes difficult to analyse dynamical properties. In particular, for logical models of biological regulatory networks, it is of real interest to study attractors and their reachability from specific initial conditions, i.e. to assess the potential asymptotical behaviours of the system. Beyond the identification of the reachable attractors, we propose to quantify this reachability. Results: Relying on the structure of the state transition graph, we estimate the probability of each attractor reachable from a given initial condition or from a portion of the state space. First, we present a quasi-exact solution with an original algorithm called Firefront, based on the exhaustive exploration of the reachable state space. Then, we introduce an adapted version of Monte Carlo simulation algorithm, termed Avatar, better suited to larger models. Firefront and Avatar methods are validated and compared to other related approaches, using as test cases logical models of synthetic and biological networks. Availability: Both algorithms are implemented as Perl scripts that can be freely downloaded from http://compbio.igc.gulbenkian.pt/nmd/node/59 along with Supplementary Material.

Abstract:
We report on some computations with reachable elements in simple Lie algebras of exceptional type within the SLA package of GAP4. These computations confirm the classification of such elements by Elashvili and Grelaud. Secondly they answer a question from Panyushev. Thirdly they show in what way a recent result of Yakimova for the Lie algebras of classical type extends to the exceptional types.