Polynomial time approximation of dense weighted instances of MAX‐CUT

We give the first polynomial time approximability characterization of denseweighted instances of MAX‐CUT, and some other dense weighted 𝒩𝒫‐hard problems in terms of their empirical weight distributions. This also gives the first almost sharp characterization of inapproximability of unweighted 0, 1 MAX‐BISECTION instances in terms of their density parameter. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 16: 314–332, 2000     

The effect of chain architecture on “sharkskin” of metallocene polyethylenes

Dynamic viscoelastic and extrusion capillary results of metallocene based polyethylenes are analyzed. Three samples show very high viscosities at low frequencies and large relaxation times, which is a symptom of the presence of small amounts of long chain branching (LCB). A linear correlation is found between the sharkskin dynamics (periodicity) and a characteristic entanglement‐disentanglement time. It is found that this correlation does not hold for samples suspected of LCB.     

MAX-CUT has a randomized approximation scheme in dense graphs

A cut in a graph G = (V(G), E(G)) is the boundary δ(S) of some subset S η V(G) and the maximum cut problem for G is to find the maximum number of edges in a cut. Let MC(G) denote this maximum. For any given 0 < α < 1, ϵ > 0, and η, we give a randomized algorithm which runs in a polynomial time and which, when applied to any given graph G on n vertices with minimum degree ≥αn, outputs a cut δ(S) of G with $ P[|\delta(S)|\geq MC(G)(1-\epsilon)] \geq 1-2^{-n} $ We also show that the proposed method can be used to approximate MAXIMUM ACYCLIC SUBGRAPH in the unweighted case. © 1996 John Wiley & Sons, Inc.     

Self-Forming Norbornene-Tetrazine Hydrogels with Independently Tunable Properties

Although photopolymerization reactions are commonly used to form hydrogels, these strategies rely on light and may not be suitable for delivering therapeutics in a minimally invasive manner. Here, hyaluronic acid (HA) macromers are modified with norbornene (Nor) or tetrazine (Tet) and upon mixing click into covalently crosslinked Nor-Tet hydrogels via a Diels–Alder reaction. By incorporating a high degree of Nor and Tet substitution, Nor-Tet hydrogels with a broad range in elastic moduli (5 to 30 kPa) and fast gelation times (1 to 5 min) are achieved. By pre-coupling methacrylated HANor macromers with thiolated peptides via a Michael addition reaction, Nor-Tet hydrogels are peptide-functionalized without affecting their physical properties. Mesenchymal stem cells (MSCs) on RGD-functionalized Nor-Tet hydrogels adhere and exhibit stiffness-dependent differences in matrix mechanosensing. Fluid properties of Nor-Tet hydrogel solutions allow for injections through narrow syringe needles and can locally deliver viable cells and peptides. Substituting HA with enzymatically degradable gelatin also results in cell-responsive Nor-Tet hydrogels, and MSCs encapsulated in Nor-Tet hydrogels preferentially differentiate into adipocytes or osteoblasts, based on 3D cellular spreading regulated by stable (HA) and degradable (gelatin) macromers.     

General Design Concepts for CAPodes as Ionologic Devices

Capacitive analogues of semiconductor diodes (CAPodes) present a new avenue for energy-efficient and nature-inspired next-generation computing devices. Here, we disclose the generalized concept for bias-direction-adjustable n- and p-CAPodes based on selective ion sieving. Controllable-unidirectional ion flux is realized by blocking electrolyte ions from entering sub-nanometer pores. The resulting CAPodes exhibit charge-storage characteristics with a high rectification ratio (96.29 %). The enhancement of capacitance is attributed to the high surface area and porosity of an omnisorbing carbon as counter electrode. Furthermore, we demonstrate the use of an integrated device in a logic gate circuit architecture to implement logic operations (‘OR’, ‘AND’). This work demonstrates CAPodes as a generalized concept to achieve p-n and n-p analogue junctions based on selective ion electrosorption, provides a comprehensive understanding and highlights applications of ion-based diodes in ionologic architectures.