Magnetic Resonance Lithography with Nanometer Resolution

We propose an approach for super-resolution optical lithography which is based on the inverse of magnetic resonance imaging (MRI). The technique uses atomic coherence in an ensemble of spin systems whose final state population can be optically detected. In principle, our method is capable of producing arbitrary one and two dimensional high-resolution patterns with high contrast

Lossy Kernelization

In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of kernelization, our definitions combine well with approximation algorithms and heuristics. The key new definition is that of a polynomial size $\alpha$-approximate kernel. Loosely speaking, a polynomial size $\alpha$-approximate kernel is a polynomial time pre-processing algorithm that takes as input an instance $(I,k)$ to a parameterized problem, and outputs another instance $(I',k')$ to the same problem, such that $|I'|+k' \leq k^{O(1)}$. Additionally, for every $c \geq 1$, a $c$-approximate solution $s'$ to the pre-processed instance $(I',k')$ can be turned in polynomial time into a $(c \cdot \alpha)$-approximate solution $s$ to the original instance $(I,k)$. Our main technical contribution are $\alpha$-approximate kernels of polynomial size for three problems, namely Connected Vertex Cover, Disjoint Cycle Packing and Disjoint Factors. These problems are known not to admit any polynomial size kernels unless $NP \subseteq coNP/poly$. Our approximate kernels simultaneously beat both the lower bounds on the (normal) kernel size, and the hardness of approximation lower bounds for all three problems. On the negative side we prove that Longest Path parameterized by the length of the path and Set Cover parameterized by the universe size do not admit even an $\alpha$-approximate kernel of polynomial size, for any $\alpha \geq 1$, unless $NP \subseteq coNP/poly$. In order to prove this lower bound we need to combine in a non-trivial way the techniques used for showing kernelization lower bounds with the methods for showing hardness of approximationComment: 58 pages. Version 2 contain new results: PSAKS for Cycle Packing and approximate kernel lower bounds for Set Cover and Hitting Set parameterized by universe siz

Contemporary Issues in Current Account Operations in Pakistani IBs - Sharia Compliant Solution

Contemporary Sharia scholars have three stances about the Current Account Operations in Pakistani Islamic Banks (IBs) i.e., (i) Ijarah based contract (ii) Wadi'ah based contract, and (iii) Qard based contract. This paper is an attempt to delve into the root causes of the differences of scholars and to find the Sharia-compliant solution acceptable for all. Descriptive as well as applied approaches are used in this paper. Clearing of ambiguity on this issue may result in twofold benefits: from the public point of view, it would satisfy practising Muslims which may result in form of huge deposits in this account (ii) from IBs viewpoint the Current Account is a bonus deposit

On the Optimality of Pseudo-polynomial Algorithms for Integer Programming

In the classic Integer Programming (IP) problem, the objective is to decide whether, for a given $m \times n$ matrix $A$ and an $m$-vector $b=(b_1,\dots, b_m)$, there is a non-negative integer $n$-vector $x$ such that $Ax=b$. Solving (IP) is an important step in numerous algorithms and it is important to obtain an understanding of the precise complexity of this problem as a function of natural parameters of the input. The classic pseudo-polynomial time algorithm of Papadimitriou [J. ACM 1981] for instances of (IP) with a constant number of constraints was only recently improved upon by Eisenbrand and Weismantel [SODA 2018] and Jansen and Rohwedder [ArXiv 2018]. We continue this line of work and show that under the Exponential Time Hypothesis (ETH), the algorithm of Jansen and Rohwedder is nearly optimal. We also show that when the matrix $A$ is assumed to be non-negative, a component of Papadimitriou's original algorithm is already nearly optimal under ETH. This motivates us to pick up the line of research initiated by Cunningham and Geelen [IPCO 2007] who studied the complexity of solving (IP) with non-negative matrices in which the number of constraints may be unbounded, but the branch-width of the column-matroid corresponding to the constraint matrix is a constant. We prove a lower bound on the complexity of solving (IP) for such instances and obtain optimal results with respect to a closely related parameter, path-width. Specifically, we prove matching upper and lower bounds for (IP) when the path-width of the corresponding column-matroid is a constant.Comment: 29 pages, To appear in ESA 201

Passive Seismic Tomography Using Induced Seismicity at a Petroleum Field in Oman

A borehole network consisting of 5 monitoring wells was used to monitor the induced seismicity at a producing petroleum field for a period of about 11 months. Nearly 5400 microseismic events were analyzed and utilized in imaging the reservoir based on a new doubledifference (DD) seismic tomography. The DD tomography method simultaneously solves for event locations and Vp, Vs, and Vp/Vs models using absolute and differential P, S and S-P arrival times. Microseismicity in the field was primarily caused by compaction of the reservoir in and above the gas bearing formation and was distributed along the two major northeastsouthwest (NE-SW) faults in the field. The model resolution analysis based on the checkerboard test and the resolution matrix showed that the central part of the model was relatively well resolved for the depth range of 0.7 to 1.1 km. Clear velocity contrasts were imaged across most parts of the two NE-SW faults. Vp/Vs ratio estimations from the tomographic inversion were low (<1.75) in the shallow depth range, likely due to lithology and gas content, whereas they were large (>1.75) in the deeper part of the model, likely due to fluid saturated formation. In this study seismic tomography showed a great potential for reservoir imaging and property estimation using induced seismicity.Petroleum Development Oma

Monitoring a Common Agent: Implications for Financial Contracting

none3We study the problem of multiple principals who want to extract income from a privately informed agent and design their contracts non-cooperatively. Our analysis reveals that the degree of coordination between principals has strong implications for the shapes of contracts. Equity like contracts and excessive monitoring emerge when principals are able to delegate monitoring or verify each others monitoring efforts. When this is not possible, free riding in monitoring weakens the incentive to monitor high profit levels, so that flat payments, debt-like contracts and very low levels of monitoring appear.mixedPARIGI B.M.; F. KHALIL; D. MARTIMORTParigi, BRUNO MARIA; F., Khalil; D., Martimor