New Complexity Results and Algorithms for the Minimum Tollbooth Problem

The inefficiency of the Wardrop equilibrium of nonatomic routing games can be eliminated by placing tolls on the edges of a network so that the socially optimal flow is induced as an equilibrium flow. A solution where the minimum number of edges are tolled may be preferable over others due to its ease of implementation in real networks. In this paper we consider the minimum tollbooth (MINTB) problem, which seeks social optimum inducing tolls with minimum support. We prove for single commodity networks with linear latencies that the problem is NP-hard to approximate within a factor of $1.1377$ through a reduction from the minimum vertex cover problem. Insights from network design motivate us to formulate a new variation of the problem where, in addition to placing tolls, it is allowed to remove unused edges by the social optimum. We prove that this new problem remains NP-hard even for single commodity networks with linear latencies, using a reduction from the partition problem. On the positive side, we give the first exact polynomial solution to the MINTB problem in an important class of graphs---series-parallel graphs. Our algorithm solves MINTB by first tabulating the candidate solutions for subgraphs of the series-parallel network and then combining them optimally

Statistical Signal Analysis for Systems with Interferenced Inputs

A new approach is introduced, based on statistical signal analysis, which overcomes the error due to input signal interference. The model analyzed is given. The input signals u sub 1 (t) and u sub 2 (t) are assumed to be unknown. The measurable signals x sub 1 (t) and x sub 2 (t) are interferened according to the frequency response functions, H sub 12 (f) and H sub 21 (f). The goal of the analysis was to evaluate the power output due to each input, u sub 1 (t) and u sub 2 (t), for the case where both are applied to the same time. In addition, all frequency response functions are calculated. The interferenced system is described by a set of five equations with six unknown functions. An IBM XT Personal Computer, which was interfaced with the FFT, was used to solve the set of equations. The software was tested on an electrical two-input, one-output system. The results were excellent. The research presented includes the analysis of the acoustic radiation from a rectangular plate with two force inputs and the sound pressure as an output signal

Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs

We consider the adjacency matrix $A$ of a large random graph and study fluctuations of the function $f_n(z,u)=\frac{1}{n}\sum_{k=1}^n\exp\{-uG_{kk}(z)\}$ with $G(z)=(z-iA)^{-1}$. We prove that the moments of fluctuations normalized by $n^{-1/2}$ in the limit $n\to\infty$ satisfy the Wick relations for the Gaussian random variables. This allows us to prove central limit theorem for $\hbox{Tr}G(z)$ and then extend the result on the linear eigenvalue statistics $\hbox{Tr}\phi(A)$ of any function $\phi:\mathbb{R}\to\mathbb{R}$ which increases, together with its first two derivatives, at infinity not faster than an exponential.Comment: 22 page

A nested alignment graph kernel through the dynamic time warping framework

In this paper, we propose a novel nested alignment graph kernel drawing on depth-based complexity traces and the dynamic time warping framework. Specifically, for a pair of graphs, we commence by computing the depth-based complexity traces rooted at the centroid vertices. The resulting kernel for the graphs is defined by measuring the global alignment kernel, which is developed through the dynamic time warping framework, between the complexity traces. We show that the proposed kernel simultaneously considers the local and global graph characteristics in terms of the complexity traces, but also provides richer statistic measures by incorporating the whole spectrum of alignment costs between these traces. Our experiments demonstrate the effectiveness and efficiency of the proposed kernel

Structural difference rule for amorphous alloy formation by ion mixing

We formulate a rule which establishes a sufficient condition that an amorphous binary alloy will be formed by ion mixing of multilayered samples when the two constituent metals are of different crystalline structure, regardless of their atomic sizes and electronegativities. The rule is supported by the experimental results we have obtained on six selected binary metal systems, as well as by the previous data reported in the literature. The amorphization mechanism is discussed in terms of the competition between two different structures resulting in frustration of the crystallization process

Search for IR Emission from Intracluster Dust in A2029

We have searched for IR emission from the intracluster dust (ICD) in the galaxy cluster A2029. Weak signals of enhanced extended emission in the cluster are detected at both 24 and 70 micron. However, the signals are indistinguishable from the foreground fluctuations. The 24 versus 70 micron color map does not discriminate the dust emission in the cluster from the cirrus emission. After excluding the contamination from the point sources, we obtain upper limits for the extended ICD emission in A2029, 5 x 10^3 Jy/sr at 24 micron and 5 x 10^4 Jy/sr at 70 micron. The upper limits are generally consistent with the expectation from theoretical calculations and support a dust deficiency in the cluster compared to the ISM in our galaxy. Our results suggest that even with the much improved sensitivity of current IR telescopes, a clear detection of the IR emission from ICD may be difficult due to cirrus noise.Comment: 5 pages, 4 figures, accepted by ApJ

Sequential nature of damage annealing and activation in implanted GaAs

Rapid thermal processing of implanted GaAs reveals a definitive sequence in the damage annealing and the electrical activation of ions. Removal of implantation-induced damage and restoration of GaAs crystallinity occurs first. Irrespective of implanted species, at this stage the GaAs is n-type and highly resistive with almost ideal values of electron mobility. Electrical activation is achieved next when, in a narrow anneal temperature window, the material becomes n- or p-type, or remains semi-insulating, commensurate to the chemical nature of the implanted ion. Such a two-step sequence in the electrical doping of GaAs by ion implantation may be unique of GaAs and other compound semiconductors

Existence problem of proton semi-bubble structure in the 21+2_1^+ state of 34^{34}Si

The fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) based on Skyrme-type interaction is used to study the existence problem of proton semi-bubble structure in the $2_1^+$ state of $^{34}$Si. The experimental excitation energy and the B(E2) strength of the $2_1^+$ state in $^{34}$Si can be reproduced quite well. The tensor effect is also studied. It is shown that the tensor interaction has a notable impact on the excitation energy of the $2_1^+$ state and a small effect on the B(E2) value. Besides, its effect on the density distributions in the ground and $2_1^+$ state of $^{34}$Si is negligible. Our present results with T36 and T44 show that the $2_1^+$ state of $^{34}$Si is mainly caused by proton transiton from $\pi 1d_{5/2}$ orbit to $\pi 2s_{1/2}$ orbit, and the existence of a proton semi-bubble structure in this state is very unlikely.Comment: 6 pages, 3 figures, 3 table