A self-powered, one-step chip for rapid, quantitative and multiplexed detection of proteins from pinpricks of whole blood

We describe an automated, self-powered chip based on lateral flow immunoassay for rapid, quantitative, and multiplex protein detection from pinpricks of whole blood. The device incorporates on-chip purification of blood plasma by employing inertial forces to focus blood cells away from the assay surface, where plasma proteins are captured and detected on antibody "barcode" arrays. Power is supplied from the capillary action of a piece of adsorbent paper, and sequentially drives, over a 40 minute period, the four steps required to capture serum proteins and then develop a multiplex immunoassay. An 11 protein panel is assayed from whole blood, with high sensitivity and high reproducibility. This inexpensive, self-contained, and easy to operate chip provides a useful platform for point-of-care diagnoses, particularly in resource-limited settings.     

Blood flow dynamics under venipuncture and viscosity estimation from pressure and flow variations

We have calculated the nonstationary flow of a viscous liquid in a narrow tube under the action of pressure variations with time. Such a flow accompanies venipuncture the procedure of taking a sample from a vein with a hypodermic needle. We show how the changes in the flow characterstics during venipuncture make it possible to actively estimate viscosity. This method is “nonperturbative” for blood in the sense that the measurement process weakly affects the measured quantity. It may find application in medicine.     

Liquid-liquid phase transformations and the shape of the melting curve

The phase diagram of elemental liquids has been found to be surprisingly rich, including variations in the melting curve and transitions in the liquid phase. The effect of these transitions in the liquid state on the shape of the melting curve is analyzed. First-order phase transitions intersecting the melting curve imply piecewise continuous melting curves, with solid-solid transitions generating upward kinks or minima and liquid-liquid transitions generating downward kinks or maxima. For liquid-liquid phase transitions proposed for carbon, phosphorous selenium, and possibly nitrogen, we find that the melting curve exhibits a kink. Continuous transitions imply smooth extrema in the melting curve, the curvature of which is described by an exact thermodynamic relation. This expression indicates that a minimum in the melting curve requires the solid compressibility to be greater than that of the liquid, a very unusual situation. This relation is employed to predict the loci of smooth maxima at negative pressures for liquids with anomalous melting curves. The relation between the location of the melting curve maximum and the two-state model of continuous liquid-liquid transitions is discussed and illustrated by the case of tellurium.     

Graphical balanced allocations and the (1 + β)‐choice process

Suppose m balls are sequentially thrown into n bins where each ball goes into a random bin. It is well‐known that the gap between the load of the most loaded bin and the average is , for large m. If each ball goes to the lesser loaded of two random bins, this gap dramatically reduces to independent of m. Consider a constrained setting where not all pairs of bins can be sampled. We are given a graph where each node corresponds to a bin. The process sequentially samples an edge from the graph and places a ball in the lesser loaded of its endpoints. We show the gap is at most where σ is the edge expansion of the graph. Our results extend naturally to the hypergraph version of this question. Our technique involves a tight analysis of what we call the “‐choice” process for some parameter : each ball goes to a random bin with probability and the lesser loaded of two random bins with probability β. For this process we show that the gap is , irrespective of m. Moreover the gap stays at in the weighted case for a large class of weight distributions. No non‐trivial bounds were previously known in the weighted case, even for the 2‐choice case. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 760–775, 2015     

Routing complexity of faulty networks

One of the fundamental problems in distributed computing is how to efficiently perform routing in a faulty network in which each link fails with some probability. This article investigates how big the failure probability can be, before the capability to efficiently find a path in the network is lost. Our main results show tight upper and lower bounds for the failure probability, which permits routing both for the hypercube and for the d‐dimensional mesh. We use tools from percolation theory to show that in the d‐dimensional mesh, once a giant component appears—efficient routing is possible. A different behavior is observed when the hypercube is considered. In the hypercube there is a range of failure probabilities in which short paths exist with high probability, yet finding them must involve querying essentially the entire network. Thus the routing complexity of the hypercube shows an asymptotic phase transition. The critical probability with respect to routing complexity lies in a different location than that of the critical probability with respect to connectivity. Finally we show that an oracle access to links (as opposed to local routing) may reduce significantly the complexity of the routing problem. We demonstrate this fact by providing tight upper and lower bounds for the complexity of routing in the random graph G_n,p. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Spectral representation of solution of cubically nonlinear equation for the Riemann simple wave

For the implicit solution to the cubically nonlinear equation of the Riemann wave (a simple wave equation), its exact explicit Fourier transform is obtained. The latter corresponds to the transformation of the initial sinusoidal profile until the discontinuity formation and, beyond it, to the asymptotic behavior of the same profile at large distances. The significance of the given solutions for the problems with cubic nonlinearity is identical to the significance of the well-known Fubini solution and the limiting version of the Fay solution for conventional nonlinear acoustics.     

On the existence and stability of business cycles in a dynamic model of a closed economy

In this paper we analyze a macroeconomic model derived from Schinasi’s model of a closed economy. Rigorous analysis of the existence and stability of the equilibrium is carried out. We present a formula for the calculation of the focus constant in the bifurcation equation of the model. Thereafter we prove the existence and stability of business cycles by application of the Hopf bifurcation theorem. Finally, we give an example of a model with a stable business cycle and its graphical illustrations.     

Surface-modified hemispherical polystyrene/polybutyl methacrylate composite particles

Micrometer-sized polystyrene/poly(n-butyl methacrylate) composite particles of hemisphere morphology and narrow size distribution were prepared by a process of single-step swelling of uniform polystyrene template microspheres with emulsion droplets of the monomer n-butyl methacrylate containing the initiator benzoyl peroxide in the presence, or absence, of the co-swelling agent toluene. Butyl methacrylate was then polymerized at 73 degrees C within the template microspheres. Surface and bulk characterization of the particles were performed by methods such as FTIR, elemental analysis, XPS, advancing contact angle, light microscope, SEM, and cross-sectional TEM. Selective surface functionalization of the poly(n-butyl methacrylate) phase of the composite particles was performed by carrying out a similar swelling and polymerization process in the presence of a water-soluble vinylic monomer such as acrylamide.