The LabMatrix system

The LabMatrix^™ is a prototyping system designed to give the user a practical and versatile platform for testing microfluidic applications in the fields of health care and life sciences. The LabMatrix^™ system consists of a microfluidic breadboard and cover that align and secure a series of specially designed LabMatrix^™ microfluidic chips. Chips are easily arranged and rearranged into a user-defined fluidic network. The LabMatrix^™ system is designed with maximum flexibility in mind, providing the user with a means to prototype a wide range of microfluidic applications in a short period.     

GigaMatrix: an ultra high-throughput tool for accessing biodiversity

Recombinant approaches for tapping into the biodiversity present in nature for the discovery of novel enzymes and biosynthetic pathways can result in large gene libraries. Likewise, laboratory evolution techniques can result in large but potentially valuable libraries. Thorough screening of these libraries requires ultra high-throughput methods. The GigaMatrix^™ screening platform addresses this opportunity using reusable high-density plates with 100,000 to 1,000,000 through-hole wells in a microplate footprint. In addition to throughputs of over 10⁷ wells per day, the platform offers a significant reduction in reagent use and waste, has fully integrated automated “cherry picking,” and uses no complicated dispensing equipment. Wells containing putative hits from targeted fluorescent liquid phase assays are revealed by a fluorescent imaging system. Vision-guided robotics are utilized to recover hits by accessing individual 200 μm and smaller wells with a disposable sterile needle. The GigaMatrix platform has proven to be an effective and efficient tool for screening gene libraries for both discovery and evolution applications.     

A generalization of the Curtis–Hedlund theorem

Let A be a set and let G be a group, and equip A^G with its prodiscrete uniform structure. Let τ:A^G→A^G be a map. We prove that τ is a cellular automaton if and only if τ is uniformly continuous and G-equivariant. We also give an example showing that a continuous and G-equivariant map τ:A^G→A^G may fail to be a cellular automaton when the alphabet set A is infinite.     

Robust stabilization of infinite dimensional systems by finite dimensional controllers

The problem of robustly stabilizing an infinite dimensional system with transfer function G, subject to an additive perturbation Δ is considered. It is assumed that: G ε ₀(σ) of systems introduced by Callier and Desoer [3]; the perturbation satisfies |W₁ΔW₂| < ε, where W₁ and W₂ are stable and minimum phase; and G and G + Δ have the same number of poles in ⁺. Now write W₁GW₂=G₁ + G₁, where G₁ is rational and totally unstable and G₂ is stable. Generalizing the finite dimensional results of Glover [12] this family of perturbed systems is shown to be stabilizable if and only if ε σ_min (G^*₁)( = the smallest Hankel singular value of G^*₁). A finite dimensional stabilizing controller is then given by where 2 is a rational approximation of G₂ such that

Full-size image

) and K₁ robustly stabilizes G₁ to margin ε. The feedback system (G, K) will then be stable if |W₁ΔW₂| _∞< ε − Δ.     

Effect of post-release sidewall morphology on the fracture and fatigue properties of polycrystalline silicon structural films

Surface properties can markedly affect the mechanical behavior of structural thin films used in microelectromechanical systems (MEMS) applications. This study highlights the striking difference in the sidewall surface morphology of n⁺-type polysilicon films from two popular MEMS processes and its effect on fracture and fatigue properties. The sidewall surface roughness was measured using atomic force microscopy, whereas silicon oxide thickness and grain size were measured using (energy-filtered) transmission electron microscopy. These measurements show that the oxide layers are not always thin native oxides, as often assumed; moreover, the roughness of the silicon/silicon oxide interface is significantly influenced by the oxidation mechanism. Thick silicon oxides (20 ± 5 nm) found in PolyMUMPs™ films are caused by galvanic corrosion from the presence of gold on the chip, whereas in SUMMiT V™ films a much thinner (3.5 ± 1.0 nm) native oxide was observed. The thicker oxide layers, in combination with differences in sidewall roughness (14 ± 5 nm for PolyMUMPs™ and 10 ± 2 nm for SUMMiT V™), can have a significant effect on the reliability of polysilicon structures subjecting to bending loads; this is shown by measurements of the fracture strength (3.8 ± 0.3 GPa for PolyMUMPs™ and 4.8 ± 0.2 GPa for SUMMiT V™) and differences in the stress-lifetime cyclic fatigue behavior.     

A system for dispensing sub-milligram doses of active pharmaceutical powders for early stage solubility assays

At early stages of drug development, the solubility of compounds is an important screening criterion. However, because scientists lack the automated tools needed to perform comprehensive early stage solubility studies, they are only able to perform a small number of experiments by hand, thus exploring only a fraction of the potential formulation design space. To allow a larger formulation design space to be explored at relatively early stages of pharmaceutical development (when 100 mg of a prototype compound is available), TransForm has created the AquaSFinX^™ and SFinX^™ micro-solubility platforms. In this article, a novel solid deposition system is described which is an enabling component of TransForm's solubility platforms. Given 100 mg of a starting material, the deposition system can dispense over six hundred 50-μg plugs of powder into 384-well or 1,536-well plates with well openings as small as 1.5 mm. Currently no commercial powder deposition system can provide this functionality. Including the time required to characterize and run the system, the dispense times range from around 2 minutes per dose for small runs involving 100 mg of starting material, to 18 seconds per dose for larger runs involving a gram or more of starting material.     

A class of projection and contraction methods for asymmetric linear variational inequalities and their relations to Fukushima's descent method

For solving asymmetric linear variational inequalities, we present a class of projection and contraction methods under the general G-norm. The search direction of our methods is just a convex combination of two descent directions of Fukushima's merit function. However, we use the direction to reduce the distance function (1/2)u − u*²_G, where μ* is a solution point of the problem. Finally, we report some numerical results for spatial price equilibrium problems by using the presented methods.     

Constructing normalisers in finite soluble groups

This paper describes algorithms for constructing a Hall π-subgroup H of a finite soluble group G and the normaliser N_G(H). If G has composition length n, then H and N_G(H) can be constructed using O(n⁴ log |G|) and O(n⁵ log |G|) group multiplications, respectively. These algorithms may be used to construct other important subgroups such as Carter subgroups, system normalisers and relative system normalisers. Computer implementations of these algorithms can compute a Sylow 3-subgroup of a group with n = 84, and its normaliser in 47 seconds and 30 seconds, respectively. Constructing normalisers of arbitrary subgroups of a finite soluble group can be complicated. This is shown by an example where constructing a normaliser is equivalent to constructing a discrete logarithm in a finite field. However, there are no known polynomial algorithms for constructing discrete logarithms.     

Grid_strain and grid_strain3: Software packages for strain field computation in 2D and 3D environments

Two Matlab™ software packages for strain field computation, starting from displacements of experimental points (EPs), are here presented. In particular, grid_strain estimates the strain on the nodes of a regular planar grid, whereas grid_strain3 operates on the points of a digital terrain model (DTM). In both cases, the computations are performed in a modified least-square approach, emphasizing the effects of nearest points. This approach allows users to operate at different scales of analysis by introducing a scale factor to reduce or also exclude points too far from grid nodes. The input data are displacements (or velocities) that can be provided by several techniques (e.g. GPS, total topographical station, terrestrial laser scanner). The analysis can be applied to both regional- and local-scale phenomena, to study tectonic crustal deformations (strain ≈10⁻⁸−10⁻⁶) or rapid landslide collapses (10⁻⁴−10²), and to characterize the kinematics of the studied system. Errors on strains and geometric significance of the results are also provided.     

A note on a problem on ω-limit sets of N–dimensional skew-product maps

In 2003, Balibrea et al. stated the problem of finding a skew-product map G on 𝕀³ holding ω _G ={0}×𝕀²=ω _G (x, y, z) for any (x, y, z)∈𝕀³, x≠0. We present a method for constructing skew-product maps F on 𝕀 ⁿ⁺¹ holding ω _F ={0}×𝕀 ⁿ =ω _F (x ₁, x ₂, …, x _n+1), (x ₁, x ₂, …, x _n+1)∈𝕀 ⁿ⁺¹, x ₁≠0.     

Floorplanning by graph dualization: L-shaped modules

We propose a novel technique for constructing a floorplan from an adjacency requirement — represented by a graphG. The algorithm finds a geometric dual ofG involving both rectangular and L-shaped modules. This is the first dualization technique which permits L-shaped modules. We can test inO(n ^3/2) time ifG admits an L-shaped dual and construct one, if it exists, inO(n ²) time, wheren is the number of modules.This work was supported in part by the National Science Foundation under Grants MIP-8709074 and MIP-8921540. The research by Yachyang Sun was done while he was with Northwestern University.     

Radiocoloring in planar graphs: Complexity and approximations

The Frequency Assignment Problem (FAP) in radio networks is the problem of assigning frequencies to transmitters, by exploiting frequency reuse while keeping signal interference to acceptable levels. The FAP is usually modelled by variations of the graph coloring problem. A Radiocoloring (RC) of a graph G(V,E) is an assignment function such that |Φ(u)-Φ(v)|2, when u,v are neighbors in G, and |Φ(u)-Φ(v)|1 when the distance of u,v in G is two. The number of discrete frequencies and the range of frequencies used are called order and span, respectively. The optimization versions of the Radiocoloring Problem (RCP) are to minimize the span or the order. In this paper we prove that the radiocoloring problem for general graphs is hard to approximate (unless NP=ZPP) within a factor of n^1/2-ε (for any ), where n is the number of vertices of the graph. However, when restricted to some special cases of graphs, the problem becomes easier. We prove that the min span RCP is NP-complete for planar graphs. Next, we provide an O(nΔ) time algorithm (|V|=n) which obtains a radiocoloring of a planar graph G that approximates the minimum order within a ratio which tends to 2 (where Δ the maximum degree of G). Finally, we provide a fully polynomial randomized approximation scheme (fpras) for the number of valid radiocolorings of a planar graph G with λ colors, in the case where λ4Δ+50.     

The complete inclusion structure of leaf power classes

Let k≥2 be an integer and G=(V,E) be a finite simple graph. A tree T is a k-leaf root of G, if V is the set of leaves of T and, for any two distinct x,yV, the distance between x and y in T is at most k if and only if xyE. We say that G is a k-leaf power if there is a k-leaf root of G. The main result of this paper is that, for all 2≤k<k^′, the classes of k- and k^′-leaf powers are inclusion-incomparable, if and only if k^′≤2k−3 and k^′−k is an odd number. With this result, an open problem from the literature about the inclusion structure of these graph classes is solved completely. In addition, the intersection of the smallest pair of inclusion-incomparable classes is studied.     

Improved upper bounds on the L(2,1) -labeling of the skew and converse skew product graphs

An L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)−f(y)|≥2 if d(x,y)=1 and |f(x)−f(y)|≥1 if d(x,y)=2, where d(x,y) denotes the distance between x and y in G. The L(2,1)-labeling number λ(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v):vV(G)}=k. Griggs and Yeh conjecture that λ(G)≤Δ² for any simple graph with maximum degree Δ≥2. This paper considers the graph formed by the skew product and the converse skew product of two graphs with a new approach on the analysis of adjacency matrices of the graphs as in [W.C. Shiu, Z. Shao, K.K. Poon, D. Zhang, A new approach to the L(2,1)-labeling of some products of graphs, IEEE Trans. Circuits Syst. II: Express Briefs (to appear)] and improves the previous upper bounds significantly.     

Some results on acyclic edge coloring of plane graphs

An acyclic edge coloring of a graph is a proper edge coloring without bichromatic cycles. The acyclic chromatic index of a graph G, denoted by α^′(G), is the minimum number k such that G admits an acyclic edge coloring using k colors. Let G be a plane graph with maximum degree Δ and girth g. In this paper, we prove that α^′(G)=Δ(G) if one of the following conditions holds: (1) Δ?8 and g?7; (2) Δ?6 and g?8; (3) Δ?5 and g?9; (4) Δ?4 and g?10; (5) Δ?3 and g?14. We also improve slightly a result of A. Fiedorowicz et al. (2008) [7] by showing that every triangle-free plane graph admits an acyclic edge coloring using at most Δ(G)+5 colors.     

Performance Analysis for Dynamic Tree Embedding ink-Partite Networks by a Random Walk

We study the problem of dynamic tree embedding ink-partite networksG^kand analyze the performance on interpartition load distribution of the embedding. We show that, for ring-connectedG^k, if the embedding proceeds by taking a unidirectional random walk at a length randomly chosen from [0, Δ − 1], where Δ is a multiple ofk, the best-case performance is achievable at probability e^−k, which is much higher than the asymptotically zero probability at which the worst-case performance may appear. We also show that the same probabilities hold for fully connectedG^kif the embedding proceeds by taking a random walk at a length randomly chosen from [2, ∞). Whenk= 2 (bipartite networks), our results show that if we do the embedding under the above random-walk schemes in their corresponding networks, we will have a 50% chance to achieve the best-case performance. We also analyze the performances for embedding in these networks in the expected case and observe the interesting fact that they match the performances in the best case when the network isk-partitionable into partitions of equal size.     

Triangular bubble spline surfaces

We present a new method for generating a Gⁿ-surface from a triangular network of compatible surface strips. The compatible surface strips are given by a network of polynomial curves with an associated implicitly defined surface, which fulfill certain compatibility conditions. Our construction is based on a new concept, called bubble patches, to represent the single surface patches. The compatible surface strips provide a simple Gⁿ-condition between two neighboring bubble patches, which are used to construct surface patches, connected with Gⁿ-continuity. For n≤2, we describe the obtained Gⁿ-condition in detail. It can be generalized to any n≥3. The construction of a single surface patch is based on Gordon–Coons interpolation for triangles.Our method is a simple local construction scheme, which works uniformly for vertices of arbitrary valency. The resulting surface is a piecewise rational surface, which interpolates the given network of polynomial curves. Several examples of G⁰, G¹ and G²-surfaces are presented, which have been generated by using our method. The obtained surfaces are visualized with reflection lines to demonstrate the order of smoothness.     

Creating change and driving innovation in highly automated and lean organizations: The Temporal Think Tank™ (T3™)

This paper introduces the concept of the temporal think tank™ (T3™), a temporary in-house research center, based on case studies with a highly automated global manufacturer and in various small-sized manufacture (SME's). The T3™ brings individuals from across the organization together in a team setting in which they are charged to look at the future, develop their decision-making skills, and use entrepreneurial thinking to incubate new processes and/or products. After an appropriate time in the temporal think tank™, the individuals are asked to return to their regular positions to implement the best practices and best ideas and doing so spur the organization forward. At intervals, the temporal think tanks™ can be reconvened, or reconstituted with new participants. This approach prepares technology champions for the SME, who can return to the organization with a fresh outlook and renewed energy to keep the enterprise at the peak of efficiency and effectiveness.     

Toward the three-dimensional structure and lysophosphatidic acid binding characteristics of the LPA4/p2y9/GPR23 receptor: A homology modeling study

Lysophosphatidic acid (LPA) is a naturally occurring phospholipid that initiates a broad array of biological processes, including those involved in cell proliferation, survival and migration via activation of specific G protein-coupled receptors located on the cell surface. To date, at least five receptor subtypes (LPA_1–5) have been identified. The LPA_1–3 receptors are members of the endothelial cell differentiation gene (Edg) family. LPA₄, a member of the purinergic receptor family, and the recently identified LPA₅ are structurally distant from the canonical Edg LPA_1–3 receptors. LPA₄ and LPA₅ are linked to G_q, G_12/13 and G_s but not G_i, while LPA_1–3 all couple to G_i in addition to G_q and G_12/13. There is also evidence that LPA₄ and LPA₅ are functionally different from the Edg LPA receptors. Computational modeling has provided useful information on the structure–activity relationship (SAR) of the Edg LPA receptors. In this work, we focus on the initial analysis of the structural and ligand-binding properties of LPA₄, a prototype non-Edg LPA receptor. Three homology models of the LPA₄ receptor were developed based on the X-ray crystal structures of the ground state and photoactivated bovine rhodopsin and the recently determined human β₂-adrenergic receptor. Docking studies of LPA in the homology models were then conducted, and plausible LPA binding loci were explored. Based on these analyses, LPA is predicted to bind to LPA₄ in an orientation similar to that reported for LPA_1–3, but through a different network of hydrogen bonds. In LPA_1–3, the ligand polar head group is reported to interact with residues at positions 3.28, 3.29 and 7.36, whereas three non-conserved amino acid residues, S114(3.28), T187(EL2) and Y265(6.51), are predicted to interact with the polar head group in the LPA₄ receptor models.     

Approximating the Minimum Chain Completion problem

A bipartite graph G=(U,V,E) is a chain graph [M. Yannakakis, Computing the minimum fill-in is NP-complete, SIAM J. Algebraic Discrete Methods 2 (1) (1981) 77–79] if there is a bijection such that Γ(π(1))Γ(π(2))Γ(π(|U|)), where Γ is a function that maps a node to its neighbors.We give approximation algorithms for two variants of the Minimum Chain Completion problem, where we are given a bipartite graph G(U,V,E), and the goal is find the minimum set of edges F that need to be added to G such that the bipartite graph G^′=(U,V,E^′) (E^′=EF) is a chain graph.