Patterns on a Roll: A Method for Continuous Feed Nanoprinting

Exploiting elastic instability in thin films has proven a robust method for creating complex patterns and structures across a wide range of lengthscales. Even the simplest of systems, an elastic membrane with a lattice of pores, under mechanical strain, generates complex patterns featuring long-range orientational order. When we promote this system to a curved surface, in particular, a cylindrical membrane, a novel set of features, patterns and broken symmetries appears. The newfound periodicity of the cylinder allows for a novel continuous method for nanoprinting.Comment: 4 pages, 4 figure

Improved Distributed Algorithms for Exact Shortest Paths

Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm of Becker et al. [DISC'17] which deterministically computes $(1+o(1))$-approximate shortest paths in $\tilde O(D+\sqrt n)$ time, where $D$ is the hop-diameter of the graph. Up to logarithmic factors, this time complexity is optimal, matching the lower bound of Elkin [STOC'04]. The question of exact shortest paths however saw no algorithmic progress for decades, until the recent breakthrough of Elkin [STOC'17], which established a sublinear-time algorithm for exact single source shortest paths on undirected graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for exact all pairs shortest paths problem on directed graphs. In this paper, we present a new single-source shortest path algorithm with complexity $\tilde O(n^{3/4}D^{1/4})$. For polylogarithmic $D$, this improves on Elkin's $\tilde{O}(n^{5/6})$ bound and gets closer to the $\tilde{\Omega}(n^{1/2})$ lower bound of Elkin [STOC'04]. For larger values of $D$, we present an improved variant of our algorithm which achieves complexity $\tilde{O}\left( n^{3/4+o(1)}+ \min\{ n^{3/4}D^{1/6},n^{6/7}\}+D\right)$, and thus compares favorably with Elkin's bound of $\tilde{O}(n^{5/6} + n^{2/3}D^{1/3} + D )$ in essentially the entire range of parameters. This algorithm provides also a qualitative improvement, because it works for the more challenging case of directed graphs (i.e., graphs where the two directions of an edge can have different weights), constituting the first sublinear-time algorithm for directed graphs. Our algorithm also extends to the case of exact $\kappa$-source shortest paths...Comment: 26 page

Joint Scheduling and Resource Allocation in CDMA Systems

Transactions on Information Theory. In this paper, the scheduling and resource allocation problem for the downlink in a CDMA-based wireless network is considered. The problem is to select a subset of the users for transmission and for each of the users selected, to choose the modulation and coding scheme, transmission power, and number of codes used. We refer to this combination as the physical layer operating point (PLOP). Each PLOP consumes different amounts of code and power resources. The resource allocation task is to pick the “optimal ” PLOP taking into account both system-wide and individual user resource constraints that can arise in a practical system. This problem is tackled as part of a utility maximization problem framed in earlier papers that includes both scheduling and resource allocation. In this setting, the problem reduces to maximizing the weighted throughput over the state-dependent downlink capacity region while taking into account the system-wide and individual user constraints. This problem is studied for the downlink of a Gaussian broadcast channel with orthogonal CDMA transmissions. This results in a tractable convex optimization problem. A dual formulation is used to obtain several key structural properties. By exploiting this structure, algorithms are developed to find the optimal solution with geometric convergence. Index Terms Cellular network, channel-aware scheduling, code division multiple access (CDMA), convex optimization, resource allocation, utility maximization. I

Generalized Ridges and Ravines on an Equiform Motion

In this paper we investigate a new type of ridges and ravines of the configuration space corresponding to an equiform motion in the Euclidean space R3. Necessary and sufficient conditions for the existence of generalized ridges and ravines are expressed as a partial differential inequalities involving the principal curvatures. For special case we obtain the solution of the differential equations which characterize some type of singularities. The singularities are displayed through figures [1, 2, 3].Key words Equiform motion; Configuration space; Generalized ridges and ravine

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Local Study of Singularities on an Equiform Motion

In this paper we investigate the local singularities of the configuration space corresponding to an equiform motion in the Euclidean space $R^3$. The chaotic behavior of singularities are displayed through figures

New Exact Jacobi Elliptic Function Solutions for Nonlinear Equations Using F-expansion Method

In this work, Jacobi elliptic function solutions for integrable nonlinear equations using F-expansion method are represented. KdV and Boussinesq equations are considered and new results are obtained.Key Words: Jacobi elliptic functions; F-expansion method; Solitary waves; Periodic solution