Permutation graphs and unique games

We study the value of unique games as a graph-theoretic parameter. This is obtained by labeling edges with permutations. We describe the classical value of a game as well as give a necessary and sufficient condition for the existence of an optimal assignment based on a generalisation of permutation graphs and graph bundles. In considering some special cases, we relate XOR games to EDGE BIPARTIZATION, and define an edge-labeling with permutations from Latin squares

Permutation graphs and unique games

We study the value of unique games as a graph-theoretic parameter. This is obtained by labeling edges with permutations. We describe the classical value of a game as well as give a necessary and sufficient condition for the existence of an optimal assignment based on a generalisation of permutation graphs and graph bundles. In considering some special cases, we relate XOR games to EDGE BIPARTIZATION, and define an edge-labeling with permutations from Latin squares

Linear game non-contextuality and Bell inequalities - a graph-theoretic approach

We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to such a game, with the constraints defining the linear game represented by an edge-coloring of the graph. We use the graph-theoretic characterization to relate the task of finding equivalent games to the notion of signed graphs and switching equivalence from graph theory. We relate the problem of computing the classical value of single-party anti-correlation XOR games to finding the edge bipartization number of a graph, which is known to be MaxSNP hard, and connect the computation of the classical value of more general XOR-d games to the identification of specific cycles in the graph. We construct an orthogonality graph of the game from the constraint graph and study its Lov\'{a}sz theta number as a general upper bound on the quantum value even in the case of single-party contextual XOR-d games. Linear games possess appealing properties for use in device-independent applications such as randomness of the local correlated outcomes in the optimal quantum strategy. We study the possibility of obtaining quantum algebraic violation of these games, and show that no finite linear game possesses the property of pseudo-telepathy leaving the frequently used chained Bell inequalities as the natural candidates for such applications. We also show this lack of pseudo-telepathy for multi-party XOR-type inequalities involving two-body correlation functions

Exploring the relationship of static and dynamic balance with muscle mechanical properties of the lower limbs in healthy young adults

There is emerging evidence that mechanical properties of in vivo muscle tissues are associated with postural sway during quiet standing. However, it is unknown if the observed relationship between mechanical properties with static balance parameters generalise to dynamic balance. Thus, we determined the relationship between static and dynamic balance parameters with muscle mechanical properties of the ankle plantar flexors [lateral gastrocnemius (GL)] and knee extensors [vastus lateralis (VL)] in vivo. Twenty-six participants (men = 16, women = 10; age = 23.3 ± 4.4 years) were assessed for static balance [centre of pressure (COP) movements during quiet standing], dynamic balance (reach distances for the Y-balance test) and mechanical properties (stiffness and tone) of the GL and VL measured in the standing and lying position. Significant (p < .05) small to moderate inverse correlations were observed between the mean COP velocity during quiet standing with stiffness (r = −.40 to −.58, p = .002 to .042) and tone (r = −0.42 to −0.56, p = 0.003 to 0.036) of the GL and VL (lying and standing). Tone and stiffness explained 16%–33% of the variance in the mean COP velocity. Stiffness and tone of the VL measured in the lying (supine) condition were also inversely significantly correlated with Y balance test performance (r = −0.39 to −0.46, p = 0.018 to 0.049). These findings highlight that individuals with low muscle stiffness and tone exhibit faster COP movements during quiet standing, indicative of reduced postural control but also reveal that low VL stiffness and tone are associated with greater reach distances in a lower extremity reaching task, indicative of greater neuromuscular performance

A disposable electrochemical immunosensor for the determination of leptin in serum and breast milk

The preparation of a disposable electrochemical immunosensor for the quantification of the hormone leptin is described in this work. The preparation approach involved immobilization of a specific biotinylated anti-leptin antibody on the surface of streptavidin-functionalized magnetic beads (StreptMBs) and a sandwich-type immunoassay involving the target analyte, monoclonal anti-leptin, and IgG labeled with alkaline phosphatase (AP-IgG). The electrochemical transduction step was accomplished by trapping the MBs bearing the immunoconjugates onto screen-printed carbon electrodes (SPCEs) by means of an Nd magnet and measuring the electrochemical oxidation of the 1-naphthol generated in the AP enzyme reaction upon 1-naphthyl phosphate (1-NPP) additions by differential pulse voltammetry (DPV). A calibration plot with a linear range between 5 and 100 pg mL 1 as well as a detection limit of 0.5 pg mL 1 (3sb/m) were achieved. This value is more than 27 times lower than that reported in the only voltammetric immunosensor for leptin described in the literature until now. The usefulness of the immunosensor was demonstrated by analyzing different types of real samples: human serum, infant powdered milk, and breast milk from a nursing mother with two months of breastfeeding

Changes in the nanoparticle aggregation rate due to the additional effect of electrostatic and magnetic forces on mass transport coefficients

The need may arise to be able to simulate the migration of groundwater nanoparticles through the ground. Transportation velocities of nanoparticles are different from that of water and depend on many processes that occur during migration. Unstable nanoparticles, such as zero-valent iron nanoparticles, are especially slowed down by aggregation between them. The aggregation occurs when attracting forces outweigh repulsive forces between the particles. In the case of iron nanoparticles that are used for remediation, magnetic forces between particles contribute to attractive forces and nanoparticles aggregate rapidly. This paper describes the addition of attractive magnetic forces and repulsive electrostatic forces between particles (by 'particle', we mean both single nanoparticles and created aggregates) into a basic model of aggregation which is commonly used. This model is created on the basis of the flow of particles in the proximity of observed particles that gives the rate of aggregation of the observed particle. By using a limit distance that has been described in our previous work, the flow of particles around one particle is observed in larger spacing between the particles. Attractive magnetic forces between particles draw the particles into closer proximity and result in aggregation. This model fits more closely with rapid aggregation which occurs between magnetic nanoparticles.Ministry of Education of the Czech Republic of the Technical University in Liberec [7822]; Ministry of Education of the Czech Republic [FR-TI1/456]; Ministry of Industry and Trad