Sensitive analysis of glutathione in bacteria and HaCaT cells by polydopamine/gold nanoparticle-coated microchip electrophoresis via online pre-concentration of field-amplified sample stacking

In this paper, polydopamine/gold nanoparticles (PDA/Au NPs) were used to construct a functional film on a glass microfluidic channel surface in microchip electrophoresis (MCE) for the separation of reduced glutathione (GSH) and oxidized glutathione (GSSH). The formation of the PDA/Au NPs was characterized by scanning electron microscopy, transmission electron microscope, UV–Vis spectra and ATR-FTIR. An online pre-concentration strategy involving field-amplified sample stacking was used to determine the sensitivity of the assay for measuring GSH and GSSH in bacteria (Escherichia coli, Staphylococcus aureus and Salmonella enterica serovar Typhimurium) and HaCaT cells samples by MCE with laser-induced fluorescence detection. The influences of the separation voltage, the concentration of the running buffer and the pH value of running buffer, were carefully investigated. Using this studied method, GSH and GSSH could be simultaneously pre-concentrated and separated within 70 s. The limits of detection of GSH and GSSH were as low as 0.81 and 0.91 nM, respectively (S/N = 3), which corresponded to approximately 180–301-fold improvements in peak height. Moreover, this method was successfully applied to the analysis of bacteria (E. coli, S. aureus and S. typhimurium) and HaCaT cell samples with a satisfactory recovery rate.     

On the <Emphasis Type="Italic">k</Emphasis>-accessibility of cores of <Emphasis Type="Italic">TU</Emphasis>-cooperative games

This paper proposes a strengthening of the author’s core-accessibility theorem for balanced TU-cooperative games. The obtained strengthening relaxes the influence of the nontransitivity of classical domination αv on the quality of the sequential improvement of dominated imputations in a game v. More specifically, we establish the k-accessibility of the core C(α _v ) of any balanced TU-cooperative game v for all natural numbers k: for each dominated imputation x, there exists a converging sequence of imputations x₀, x₁,..., such that x₀ = x, lim x _r ∈ C(α _v ) and x_r?m is dominated by any successive imputation x _r with m ∈ [1, k] and r ≥ m. For showing that the TU-property is essential to provide the k-accessibility of the core, we give an example of an NTU-cooperative game G with a ”black hole” representing a nonempty closed subset B ? G(N) of dominated imputations that contains all the α _G -monotonic sequential improvement trajectories originating at any point x ∈ B.     

Some properties of the disjunctive languages contained in <Emphasis Type="Italic">Q</Emphasis>

The set of all primitive words Q over an alphabet X was first defined and studied by Shyr and Thierrin (Proceedings of the 1977 Inter. FCT-Conference, Poznan, Poland, Lecture Notes in Computer Science 56. pp. 171–176 (1977)). It showed that for the case |X| ≥ 2, the set along with \({Q^{(i)} = \{f^i\,|\,f \in Q\}, i\geq 2}\) are all disjunctive. Since then these disjunctive sets are often be quoted. Following Shyr and Thierrin showed that the half sets \({Q_{ev} = \{f \in Q\,|\,|f| = {\rm even}\}}\) and Q _od = Q \ Q _ev of Q are disjunctive, Chien proved that each of the set \({Q_{p,r}= \{u\in Q\,|\,|u|\equiv r\,(mod\,p) \},\,0\leq r < p}\) is disjunctive, where p is a prime number. In this paper, we generalize this property to that all the languages \({Q_{n,r}= \{u\in Q\,|\,|u|\equiv r\,(mod\,n) \},\, 0\leq r < n}\) are disjunctive languages, where n is any positive integer. We proved that for any n ≥ 1, k ≥ 2, (Q _n,0) ^k are all regular languages. Some algebraic properties related to the family of languages {Q _n,r | n ≥ 2, 0 ≤ r < n } are investigated.     

Locally adaptive <Emphasis Type="Italic">k</Emphasis> parameter selection for nearest neighbor classifier: one nearest cluster

The k nearest neighbors (k-NN) classification technique has a worldly wide fame due to its simplicity, effectiveness, and robustness. As a lazy learner, k-NN is a versatile algorithm and is used in many fields. In this classifier, the k parameter is generally chosen by the user, and the optimal k value is found by experiments. The chosen constant k value is used during the whole classification phase. The same k value used for each test sample can decrease the overall prediction performance. The optimal k value for each test sample should vary from others in order to have more accurate predictions. In this study, a dynamic k value selection method for each instance is proposed. This improved classification method employs a simple clustering procedure. In the experiments, more accurate results are found. The reasons of success have also been understood and presented.     

Developing heatable microfluidic chip to generate gelatin emulsions and microcapsules

The heatable microfluidic chip developed herein successfully integrates a microheater and flow-focusing device to generate uniform-sized gelatin emulsions under various flow rate ratios (sample phase/oil phase, Q _s/Q _o) and driven voltages. The gelatin emulsions can be applied to encapsulate vitamin C for drug release. Our goal is to create the thermal conditions for thermo-sensitive hydrogel materials in the microfluidic chip and generate continuous and uniform emulsions under any external environment. The gelatin emulsion sizes have a coefficient of variation of <5 % and can be precisely controlled by altering the flow rate ratio (Q _s/Q _o) and driven voltage. The gelatin emulsion diameters range from 45 to 120 μm. Moreover, various sizes of these gelatin microcapsules containing vitamin C were used for drug release. The developed microfluidic chip has the advantages of a heatable platform in the fluid device, active control over the emulsion diameter, the generation of uniform-sized emulsions, and simplicity. This new approach for gelatin microcapsules will provide many potential applications in drug delivery and pharmaceuticals.     

Hydrodynamic focusing and interdistance control of particle-laden flow for microflow cytometry

Single-file focusing and minimum interdistance of micron-size objects in a sample is a prerequisite for accurate flow cytometry measurements. Here, we report analytical models for predicting the focused width of a sample stream b as a function of channel aspect ratio α, sheath-to-sample flow rate ratio f and viscosity ratio λ in both 2D and 3D focusing. We present another analytical model to predict spacing between an adjacent pair of objects in a focused sample stream as a function of sample concentration C, mobility ? of the objects in the prefocused and postfocused regions and flow rate ratio f in both 2D and 3D flow focusing. Numerical simulations are performed using Ansys Fluent VOF model to predict the width of sample stream in 2D and 3D hydrodynamic focusing for different sample-to-sheath viscosity ratios, aspect ratios and flow rate ratios. Experiments are performed on both planar and three-dimensional devices fabricated in PDMS to demonstrate focusing of sample stream and spacing of polystyrene beads in the unfocused and focused stream at different sample concentrations C. The predictions of the analytical model and simulations are compared with experimental data, and a good match is found (within 12 %). Further, mobility of objects is experimentally studied in 2D and 3D focusing, and the spread of the mobility data is used as tool for the demonstration of particle focusing in flow cytometer applications.     

Star reduction among minimal length addition chains

An addition chain for a natural number n is a sequence \({1=a_0 < a_1 < \cdots < a_r=n}\) of numbers such that for each 0 < i ≤ r, a _i  = a _j  + a _k for some 0 ≤ k ≤ j < i. The minimal length of an addition chain for n is denoted by ?(n). If j = i ? 1, then step i is called a star step. We show that there is a minimal length addition chain for n such that the last four steps are stars. Then we conjecture that there is a minimal length addition chain for n such that the last \({\lfloor\frac{\ell(n)}{2}\rfloor}\)-steps are stars. We verify that the conjecture is true for all numbers up to 2¹⁸. An application of the result and the conjecture to generate a minimal length addition chain reduce the average CPU time by 23–29% and 38–58% respectively, and memory storage by 16–18% and 26–45% respectively for m-bit numbers with 14 ≤ m ≤ 22.     

The Number of Tree Stars Is <Emphasis Type="Italic">O</Emphasis><Superscript>*</Superscript>(1.357<Superscript><Emphasis Type="Italic">k</Emphasis></Superscript>)

Every rectilinear Steiner tree problem admits an optimal tree T ^* which is composed of tree stars. Moreover, the currently fastest algorithms for the rectilinear Steiner tree problem proceed by composing an optimum tree T ^* from tree star components in the cheapest way. The efficiency of such algorithms depends heavily on the number of tree stars (candidate components). Fößmeier and Kaufmann (Algorithmica 26, 68–99, 2000) showed that any problem instance with k terminals has a number of tree stars in between 1.32 ^k and 1.38 ^k (modulo polynomial factors) in the worst case. We determine the exact bound O ^*(ρ ^k ) where ρ≈1.357 and mention some consequences of this result.     

(<Emphasis Type="Italic">a</Emphasis>, <Emphasis Type="Italic">d</Emphasis>)-Distance Antimagic Labeling of Some Types of Graphs

We analyze the necessary existence conditions for (a, d)-distance antimagic labeling of a graph G = (V, E) of order n. We obtain theorems that expand the family of not (a, d) -distance antimagic graphs. In particular, we prove that the crown P _n ○ P ₁ does not admit an (a, 1)-distance antimagic labeling for n ≥ 2 if a ≥ 2. We determine the values of a at which path P _n can be an (a, 1)-distance antimagic graph. Among regular graphs, we investigate the case of a circulant graph.     

On Supersymmetric M-brane configurations with an R<Stack><Subscript>*</Subscript><Superscript>1,1</Superscript></Stack> /Z<Subscript>2</Subscript> submanifold

We obtain new examples of partly supersymmetric M-brane solutions defined on products of Ricci-flat manifolds, which contain a two-dimensional Lorentzian submanifold R _* ^1,1 /Z ₂ with one parallel spinor. The examples belong to the following configurations: M2, M5, M2 ∩M5 and M5 ∩M5. Among them, an M2 solution with N = 1/32 fractional number of preserved supersymmetries is presented.     

Deterministic lateral displacement (DLD) in the high Reynolds number regime: high-throughput and dynamic separation characteristics

Recent progress in the development of biosensors has created a demand for high-throughput sample preparation techniques that can be easily integrated into microfluidic or lab-on-a-chip platforms. One mechanism that may satisfy this demand is deterministic lateral displacement (DLD), which uses hydrodynamic forces to separate particles based on size. Numerous medically relevant cellular organisms, such as circulating tumor cells (10–15 µm) and red blood cells (6–8 µm), can be manipulated using microscale DLD devices. In general, these often-viscous samples require some form of dilution or other treatment prior to microfluidic transport, further increasing the need for high-throughput operation to compensate for the increased sample volume. However, high-throughput DLD devices will require a high flow rate, leading to an increase in Reynolds numbers (Re) much higher than those covered by existing studies for microscale (≤?100 µm) DLD devices. This study characterizes the separation performance for microscale DLD devices in the high-Re regime (10?<?Re?<?60) through numerical simulation and experimental validation. As Re increases, streamlines evolve and microvortices emerge in the wake of the pillars, resulting in a particle trajectory shift within the DLD array. This differs from previous DLD works, in that traditional models only account for streamlines that are characteristic of low-Re flow, with no consideration for the transformation of these streamlines with increasing Re. We have established a trend through numerical modeling, which agrees with our experimental findings, to serve as a guideline for microscale DLD performance in the high-Re regime. Finally, this new phenomenon could be exploited to design passive DLD devices with a dynamic separation range, controlled simply by adjusting the device flow rate.     

Error bounds for complementarity problems with tridiagonal nonlinear functions

In this paper we consider the complementarity problem NCP(f) with f(x) = Mx + φ(x), where M ∈ R ^n×n is a real matrix and φ is a so-called tridiagonal (nonlinear) mapping. This problem occurs, for example, if certain classes of free boundary problems are discretized. We compute error bounds for approximations \({\hat x}\) to a solution x* of the discretized problems. The error bounds are improved by an iterative method and can be made arbitrarily small. The ideas are illustrated by numerical experiments.     

On (<Emphasis Type="Italic">a</Emphasis>, <Emphasis Type="Italic">d</Emphasis> )-Distance Anti-Magic and 1-Vertex Bimagic Vertex Labelings of Certain Types of Graphs

The results for the corona P _n ?°?P₁ are generalized, which make it possible to state that P _n ?°?P₁ is not an ( a, d)-distance antimagic graph for arbitrary values of a and d. A condition for the existence of an ( a, d)-distance antimagic labeling of a hypercube Q _n is obtained. Functional dependencies are found that generate this type of labeling for Q _n . It is proved by the method of mathematical induction that Q _n is a (2 ⁿ ?+?n???1,?n???2) -distance antimagic graph. Three types of graphs are defined that do not allow a 1-vertex bimagic vertex labeling. A relation between a distance magic labeling of a regular graph G and a 1-vertex bimagic vertex labeling of G?∪?G is established.     

<Emphasis Type="Italic">α</Emphasis>-Systems of differential inclusions and their unification

This paper introduces α-systems of differential inclusions on a bounded time interval [t₀, ?] and defines α-weakly invariant sets in [t₀, ?] × ?_n, where ?_n is a phase space of the differential inclusions. We study the problems connected with bringing the motions (trajectories) of the differential inclusions from an α-system to a given compact set M ? ?_n at the moment ? (the approach problems). The issues of extracting the solvability set W ? [t₀, ?] × ?ⁿ in the problem of bringing the motions of an α-system to M and the issues of calculating the maximal α-weakly invariant set W^c ? [t₀, ?] × ?ⁿ are also discussed. The notion of the quasi-Hamiltonian of an α-system (α-Hamiltonian) is proposed, which seems important for the problems of bringing the motions of the α-system to M.     

Parallel <Emphasis Type="Italic">LL</Emphasis> parsing

A deterministic parallel LL parsing algorithm is presented. The algorithm is based on a transformation from a parsing problem to parallel reduction. First, a nondeterministic version of a parallel LL parser is introduced. Then, it is transformed into the deterministic version—the LLP parser. The deterministic LLP(q,k) parser uses two kinds of information to select the next operation — a lookahead string of length up to k symbols and a lookback string of length up to q symbols. Deterministic parsing is available for LLP grammars, a subclass of LL grammars. Since the presented deterministic and nondeterministic parallel parsers are both based on parallel reduction, they are suitable for most parallel architectures.     

Noise Level Estimation in High-Dimensional Linear Models

We consider the problem of estimating the noise level σ² in a Gaussian linear model Y = Xβ+σξ, where ξ ∈ ?ⁿ is a standard discrete white Gaussian noise and β ∈ ?^p an unknown nuisance vector. It is assumed that X is a known ill-conditioned n × p matrix with n ≥ p and with large dimension p. In this situation the vector β is estimated with the help of spectral regularization of the maximum likelihood estimate, and the noise level estimate is computed with the help of adaptive (i.e., data-driven) normalization of the quadratic prediction error. For this estimate, we compute its concentration rate around the pseudo-estimate ||Y ? Xβ||²/n.     

Novel steganographic method based on generalized <Emphasis Type="Italic">K</Emphasis>-distance <Emphasis Type="Italic">N</Emphasis>-dimensional pixel matching

In this paper, a steganographic scheme adopting the concept of the generalized K _d -distance N-dimensional pixel matching is proposed. The generalized pixel matching embeds a B-ary digit (B is a function of K and N) into a cover vector of length N, where the order-d Minkowski distance-measured embedding distortion is no larger than K. In contrast to other pixel matching-based schemes, a N-dimensional reference table is used. By choosing d, K, and N adaptively, an embedding strategy which is suitable for arbitrary relative capacity can be developed. Additionally, an optimization algorithm, namely successive iteration algorithm (SIA), is proposed to optimize the codeword assignment in the reference table. Benefited from the high dimensional embedding and the optimization algorithm, nearly maximal embedding efficiency is achieved. Compared with other content-free steganographic schemes, the proposed scheme provides better image quality and statistical security. Moreover, the proposed scheme performs comparable to state-of-the-art content-based approaches after combining with image models.     

Testing list <Emphasis Type="Italic">H</Emphasis>-homomorphisms

In the List H- Homomorphism Problem, for a graph H that is a parameter of the problem, an instance consists of an undirected graph G with a list constraint \({L(v) \subseteq V(H)}\) for each variable \({v \in V(G)}\), and the objective is to determine whether there is a list H-homomorphism \({f:V(G) \to V(H)}\), that is, \({f(v) \in L(v)}\) for every \({v \in V(G)}\) and \({(f(u),f(v)) \in E(H)}\) whenever \({(u,v) \in E(G)}\).We consider the problem of testing list H-homomorphisms in the following weighted setting: An instance consists of an undirected graph G, list constraints L, weights imposed on the vertices of G, and a map \({f:V(G) \to V(H)}\) given as an oracle access. The objective is to determine whether f is a list H-homomorphism or far from any list H-homomorphism. The farness is measured by the total weight of vertices \({v \in V(G)}\) for which f(v) must be changed so as to make f a list H-homomorphism. In this paper, we classify graphs H with respect to the number of queries to f required to test the list H-homomorphisms. Specifically, we show that (i) list H-homomorphisms are testable with a constant number of queries if and only if H is a reflexive complete graph or an irreflexive complete bipartite graph and (ii) list H-homomorphisms are testable with a sublinear number of queries if and only if H is a bi-arc graph.     

On transitive partitions of an <Emphasis Type="Italic">n</Emphasis>-cube into codes

We present methods to construct transitive partitions of the set E ⁿ of all binary vectors of length n into codes. In particular, we show that for all n = 2 ^k ? 1, k ≥ 3, there exist transitive partitions of E ⁿ into perfect transitive codes of length n.     

Protecting query privacy with differentially private <Emphasis Type="Italic">k</Emphasis>-anonymity in location-based services

Nowadays, location-based services (LBS) are facilitating people in daily life through answering LBS queries. However, privacy issues including location privacy and query privacy arise at the same time. Existing works for protecting query privacy either work on trusted servers or fail to provide sufficient privacy guarantee. This paper combines the concepts of differential privacy and k-anonymity to propose the notion of differentially private k-anonymity (DPkA) for query privacy in LBS. We recognize the sufficient and necessary condition for the availability of 0-DPkA and present how to achieve it. For cases where 0-DPkA is not achievable, we propose an algorithm to achieve ??-DPkA with minimized ??. Extensive simulations are conducted to validate the proposed mechanisms based on real-life datasets and synthetic data distributions.