A Dissipative Reaction Network Drives Transient Solid–Liquid and Liquid–Liquid Phase Cycling of Nanoparticles

Transient states maintained by energy dissipation are an essential feature of dynamic systems where structures and functions are regulated by fluxes of energy and matter through chemical reaction networks. Perfected in biology, chemically fueled dissipative networks incorporating nanoscale components allow the unique properties of nanomaterials to be bestowed with spatiotemporal adaptability and chemical responsiveness. We report the transient dispersion of gold nanoparticles in water, powered by dissipation of a chemical fuel. A dispersed state that is generated under non-equilibrium conditions permits fully reversible solid–liquid or liquid–liquid phase transfer. The molecular basis of the out-of-equilibrium process is reversible covalent modification of nanoparticle-bound ligands by a simple inorganic activator. Activator consumption by a coupled dissipative reaction network leads to autonomous cycling between phases. The out-of-equilibrium lifetime is tunable by adjusting the pH value, and reversible phase cycling is reproducible over several cycles.     

Mechano-Activated Self-Immolation of Hydrogels via Signal Amplification

Cellular organisms possess intricate mechano-adaptive systems that enable them to sense forces and process them with (bio)chemical circuits for functional adaptation. Inspired by such processes, this study introduces a hydrogel system capable of mechanically activated and chemically transduced self-destruction. Our judiciously designed hydrogels can mechanically generate radicals that are processed and amplified in a self-propagating radical de-crosslinking reaction, ultimately leading to mechanically triggered self-immolation. We put such systems to work in mechano-induced debonding, and in a bilayer actuator, where swelling-induced bending generates sufficient force for selective degradation of one layer, leading to autonomous self-regulation associated with unbending. Our work helps define design criteria for molecularly controlled adaptive and self-regulating materials with embodied mechano-chemical information processing, and showcases their potential for adhesives and soft robotics.     

Stability analysis of switched homogeneous time-delay systems under synchronous and asynchronous commutation

In this work, stability analysis for a class of switched nonlinear time-delay systems is performed by applying Lyapunov–Krasovskii and Lyapunov–Razumikhin approaches. It is assumed that each subsystem in the family is homogeneous (of positive or negative degree) and asymptotically stable in the delay-free setting. The cases of existence of a common or multiple Lyapunov–Krasovskii functionals and a common Lyapunov–Razumikhin function are explored. The scenarios with synchronous and asynchronous switching are considered, and it is demonstrated that depending on the kind of commutation, one of the frameworks for stability analysis outperforms another, but finally leading to similar restrictions for both types of switching (despite the asynchronous one seems to be more demanded). The obtained results are applied to mechanical systems having restoring forces with real-valued powers.     

Stabilization of switched systems with polytopic uncertainties via composite quadratic functions

This paper studied the stabilization of switched linear systems with polytopic uncertainties by employing the methods of nonsmooth analysis and the composite quadratic Lyapunov functions. Above all, the minimum quadratic functions and the directional derivatives along the vertex directions of subsystems are applied to construct the new switching law. Then, some sufficient conditions for stabilization of switched linear systems are established considering the sliding modes and the directional derivatives along sliding modes. Finally, numerical examples are given to demonstrate the effectiveness of the synthesis results.     

关于两个P-值逻辑函数的和函数的Chrestenson谱公式

类似于两个布尔函数的和函数的ｗａｌｓｈ谱公式,本文给出了两个３－值、５－值、７－值逻辑函数和函数的Ｃｈｒｅｓｔｅｎｓｏｎ谱公式。     

Term rank preservers of Boolean matrices

We obtain some characterizations of linear operators that preserve the term rank of Boolean matrices. That is, a linear operator over Boolean matrices preserves the term rank if and only if it preserves the term ranks 1 and k(≠1) if and only if it preserves the term ranks 2 and l(≠2). Other characterizations of term rank preservers are given.     

Logic Regression

Logic regression is an adaptive regression methodology that attempts to construct predictors as Boolean combinations of binary covariates. In many regression problems a model is developed that relates the main effects (the predictors or transformations thereof) to the response, while interactions are usually kept simple (two- to three-way interactions at most). Often, especially when all predictors are binary, the interaction between many predictors may be what causes the differences in response. This issue arises, for example, in the analysis of SNP microarray data or in some data mining problems. In the proposed methodology, given a set of binary predictors we create new predictors such as “X₁, X₂, X³, and X⁴ are true,” or “X⁵ or X⁶ but not X⁷ are true.” In more specific terms: we try to fit regression models of the form g(E[Y]) = b₀ + b₁ L₁ + · · · + b_n L_n , where L_j is any Boolean expression of the predictors. The L_j and b_j are estimated simultaneously using a simulated annealing algorithm. This article discusses how to fit logic regression models, how to carry out model selection for these models, and gives some examples.     

Split Orthogonal Arrays and Maximum Independent Resilient Systems of Functions

A system of (Boolean) functions in variables is called randomized if the functions preserve the property of their variables to be independent and uniformly distributed random variables. Such a system is referred to as -resilient if for any substitution of constants for any variables, where 0 i t, the derived system of functions in variables will be also randomized. We investigate the problem of finding the maximum number of functions in variables of which any form a -resilient system. This problem is reduced to the minimization of the size of certain combinatorial designs, which we call split orthogonal arrays. We extend some results of design and coding theory, in particular, a duality in bounding the optimal sizes of codes and designs, in order to obtain upper and lower bounds on . In some cases, these bounds turn out to be very tight. In particular, for some infinite subsequences of integers they allow us to prove that , , , , . We also find a connection of the problem considered with the construction of unequal-error-protection codes and superimposed codes for multiple access in the Hamming channel.     

The Zero-Divisor Graphs Which Are Uniquely Determined By Neighborhoods

A nonempty simple connected graph G is called a uniquely determined graph, if distinct vertices of G have distinct neighborhoods. We prove that if R is a commutative ring, then Γ(R) is uniquely determined if and only if either R is a Boolean ring or T(R) is a local ring with x² = 0 for any x ∈ Z(R), where T(R) is the total quotient ring of R. We determine all the corresponding rings with characteristic p for any finite complete graph, and in particular, give all the corresponding rings of K_n if n + 1 = p^q for some primes p, q. Finally, we show that a graph G with more than two vertices has a unique corresponding zero-divisor semigroup if G is a zero-divisor graph of some Boolean ring.     

Global exponential stability of certain switched systems with time-varying delays

This paper is focused on global exponential stability of certain switched systems with time-varying delays. By using an average dwell time (ADT) approach that is different from the method in [P.H.A. Ngoc, On exponential stability of nonlinear differential systems with time-varying delay, Applied Mathematics Letters 25 (2012) 1208–1213], we establish a new global exponential stability criterion for the switched linear time-delay system under the ADT switching. We also apply this method to a general switched nonlinear time-delay system. A numerical example is given to show the effectiveness of our results.