Exchange operator formalism for N-body spin models with near-neighbors interactions

We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finite-dimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials.Comment: RevTeX, 31 pages, no figures; important additional conten

Quasi-exactly Solvable Lie Superalgebras of Differential Operators

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is nontrivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of QES quantum mechanical models for spin 1/2 particles in one dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page

Forward Analysis and Model Checking for Trace Bounded WSTS

We investigate a subclass of well-structured transition systems (WSTS), the bounded---in the sense of Ginsburg and Spanier (Trans. AMS 1964)---complete deterministic ones, which we claim provide an adequate basis for the study of forward analyses as developed by Finkel and Goubault-Larrecq (Logic. Meth. Comput. Sci. 2012). Indeed, we prove that, unlike other conditions considered previously for the termination of forward analysis, boundedness is decidable. Boundedness turns out to be a valuable restriction for WSTS verification, as we show that it further allows to decide all $\omega$-regular properties on the set of infinite traces of the system

Self-processes in interdependent relationships: Partner affirmation and the Michelangelo Phenomenon

This essay reviews theory and research regarding the "Michelangelo phenomenon," which describes the manner in which close partners shape one another's dispositions, values, and behavioral tendencies. Individuals are more likely to exhibit movement toward their ideal selves to the degree that their partners exhibit affirming perception and behavior, exhibiting confidence in the self 's capacity and enacting behaviors that elicit key features of the self 's ideal. In turn, movement towards the ideal self yields enhanced personal well-being and couple well-being. We review empirical evidence regarding this phenomenon and discuss self and partner variables that contribute to the process. © John Benjamins Publishing Company

The Parametric Ordinal-Recursive Complexity of Post Embedding Problems

Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine the construction of Chambart and Schnoebelen (LICS 2008) and prove parametric lower bounds depending on the size of the alphabet.Comment: 16 + vii page

A New Algebraization of the Lame Equation

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page

Whole lifespan microscopic observation of budding yeast aging through a microfluidic dissection platform

Important insights into aging have been generated with the genetically tractable and short-lived budding yeast. However, it is still impossible today to continuously track cells by high-resolution microscopic imaging (e.g., fluorescent imaging) throughout their entire lifespan. Instead, the field still needs to rely on a 50-y-old laborious and time-consuming method to assess the lifespan of yeast cells and to isolate differentially aged cells for microscopic snapshots via manual dissection of daughter cells from the larger mother cell. Here, we are unique in achieving continuous and high-resolution microscopic imaging of the entire replicative lifespan of single yeast cells. Our microfluidic dissection platform features an optically prealigned single focal plane and an integrated array of soft elastomer-based micropads, used together to allow for trapping of mother cells, removal of daughter cells, monitoring gradual changes in aging, and unprecedented microscopic imaging of the whole aging process. Using the platform, we found remarkable age-associated changes in phenotypes (e.g., that cells can show strikingly differential cell and vacuole morphologies at the moment of their deaths), indicating substantial heterogeneity in cell aging and death. We envision the microfluidic dissection platform to become a major tool in aging research.

Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata

Safety verification of asynchronous pushdown systems with shaped stacks

In this paper, we study the program-point reachability problem of concurrent pushdown systems that communicate via unbounded and unordered message buffers. Our goal is to relax the common restriction that messages can only be retrieved by a pushdown process when its stack is empty. We use the notion of partially commutative context-free grammars to describe a new class of asynchronously communicating pushdown systems with a mild shape constraint on the stacks for which the program-point coverability problem remains decidable. Stacks that fit the shape constraint may reach arbitrary heights; further a process may execute any communication action (be it process creation, message send or retrieval) whether or not its stack is empty. This class extends previous computational models studied in the context of asynchronous programs, and enables the safety verification of a large class of message passing programs