Solving Gapped Hamiltonians Locally

We show that any short-range Hamiltonian with a gap between the ground and excited states can be written as a sum of local operators, such that the ground state is an approximate eigenvector of each operator separately. We then show that the ground state of any such Hamiltonian is close to a generalized matrix product state. The range of the given operators needed to obtain a good approximation to the ground state is proportional to the square of the logarithm of the system size times a characteristic "factorization length". Applications to many-body quantum simulation are discussed. We also consider density matrices of systems at non-zero temperature.Comment: 13 pages, 2 figures; minor changes to references, additional discussion of numerics; additional explanation of nonzero temperature matrix product for

Nested reconfigurable robots: theory, design, and realization

Rather than the conventional classification method, we propose to divide modular and reconfigurable robots into intra-, inter-, and nested reconfigurations. We suggest designing the robot with nested reconfigurability, which utilizes individual robots with intra-reconfigurability capable of combining with other homogeneous/heterogeneous robots (inter-reconfigurability). The objective of this approach is to generate more complex morphologies for performing specific tasks that are far from the capabilities of a single module or to respond to programmable assembly requirements. In this paper, we discuss the theory, concept, and initial mechanical design of Hinged-Tetro, a self-reconfigurable module conceived for the study of nested reconfiguration. Hinged-Tetro is a mobile robot that uses the principle of hinged dissection of polyominoes to transform itself into any of the seven one-sided tetrominoes in a straightforward way. The robot can also combine with other modules for shaping complex structures or giving rise to a robot with new capabilities. Finally, the validation experiments verify the nested reconfigurability of Hinged-Tetro. Extensive tests and analyses of intra-reconfiguration are provided in terms of energy and time consumptions. Experiments using two robots validate the inter-reconfigurability of the proposed module

(E)-N-(Anthracen-9-yl­methyl­idene)-4-nitro­aniline

In the title molecule, C21H14N2O2, the anthracenyl system is approximately planar [maximum deviation = 0.056 (4) Å] and is oriented at a dihedral angle of 73.6 (1)° with respect to the benzene ring. An intra­molecular C—H⋯N hydrogen bond generates an S(6) ring motif. The crystal packing is stabilized by C—H⋯π and π–π inter­actions [centroid–centroid distances of 3.688 (2), 3.656 (1) and 3.716 (2) Å]

Enumeration of simple random walks and tridiagonal matrices

We present some old and new results in the enumeration of random walks in one dimension, mostly developed in works of enumerative combinatorics. The relation between the trace of the $n$-th power of a tridiagonal matrix and the enumeration of weighted paths of $n$ steps allows an easier combinatorial enumeration of the paths. It also seems promising for the theory of tridiagonal random matrices .Comment: several ref.and comments added, misprints correcte

Functional losses in ground spider communities due to habitat structure degradation under tropical land-use change

Deforestation and land‐use change in tropical regions result in habitat loss and extinction of species that are unable to adapt to the conditions in agricultural landscapes. If the associated loss of functional diversity is not compensated by species colonizing the converted habitats, extinctions might be followed by a reduction or loss of ecosystem functions including biological control. To date, little is known about how land‐use change in the tropics alters the functional diversity of invertebrate predators and which key environmental factors may mitigate the decline in functional diversity and predation in litter and soil communities. We applied litter sieving and heat extraction to study ground spider communities and assessed structural characteristics of vegetation and parameters of litter in rainforest and agricultural land‐use systems (jungle rubber, rubber, and oil palm monocultures) in a Southeast Asian hotspot of rainforest conversion: Sumatra, Indonesia. We found that (1) spider density, species richness, functional diversity, and community predation (energy flux to spiders) were reduced by 57–98% from rainforest to oil palm monoculture; (2) jungle rubber and rubber monoculture sustained relatively high diversity and predation in ground spiders, but small cryptic spider species strongly declined; (3) high species turnover compensated losses of some functional trait combinations, but did not compensate for the overall loss of functional diversity and predation per unit area; (4) spider diversity was related to habitat structure such as amount of litter, understory density, and understory height, while spider predation was better explained by plant diversity. Management practices that increase habitat‐structural complexity and plant diversity such as mulching, reduced weeding, and intercropping monocultures with other plants may contribute to maintaining functional diversity of and predation services provided by ground invertebrate communities in plantations

Application of Wear-Resistant, NanoComposite Coatings Produced from Iron-Based Glassy Powders

This report talks about Application of Wear-Resistant, NanoComposite Coatings Produced from Iron-Based Glassy Powders

Boolean dynamics revisited through feedback interconnections

Boolean models of physical or biological systems describe the global dynamics of the system and their attractors typically represent asymptotic behaviors. In the case of large networks composed of several modules, it may be difficult to identify all the attractors. To explore Boolean dynamics from a novel viewpoint, we will analyse the dynamics emerging from the composition of two known Boolean modules. The state transition graphs and attractors for each of the modules can be combined to construct a new asymptotic graph which will (1) provide a reliable method for attractor computation with partial information; (2) illustrate the differences in dynamical behavior induced by the updating strategy (asynchronous, synchronous, or mixed); and (3) show the inherited organization/structure of the original network’s state transition graph.publishe

Scalar Ambiguity and Freeness in Matrix Semigroups over Bounded Languages

There has been much research into freeness properties of finitely generated matrix semigroups under various constraints, mainly related to the dimensions of the generator matrices and the semiring over which the matrices are defined. A recent paper has also investigated freeness properties of matrices within a bounded language of matrices, which are of the form M1M2 · · · Mk ⊆ F n×n for some semiring F [9]. Most freeness problems have been shown to be undecidable starting from dimension three, even for upper-triangular matrices over the natural numbers. There are many open problems still remaining in dimension two. We introduce a notion of freeness and ambiguity for scalar reachability problems in matrix semigroups and bounded languages of matrices. Scalar reachability concerns the set {ρ TMτ |M ∈ S}, where ρ, τ ∈ F n are vectors and S is a finitely generated matrix semigroup. Ambiguity and freeness problems are defined in terms of uniqueness of factorizations leading to each scalar. We show various undecidability results

Institutional distance and foreign subsidiary performance in emerging markets: moderating effects of ownership strategy and host-country experience

Institutional distance has been known to be an important driver of Multinational Enterprises’ strategies and performance in host countries. Based on a large panel dataset of 10562 firms operating in 17 emerging markets and spanning 80 home countries, we re-examine the relationship described by Gaur and Lu (2007) between regulatory institutional distance and subsidiary performance. We extend this research by (1) examining this relationship in the context of emerging markets, (2) examining the moderating effects of ownership strategy and host-country experience within the context of emerging markets and (3) accounting for a greater variety of institutions by including a large number of home and host countries. We find that institutional distance negatively affects subsidiary performance in emerging markets. Our findings also show that the negative effects of institutional distance on subsidiary performance are lesser for subsidiaries with partial ownership (than for subsidiaries with full ownership) and for subsidiaries with greater host-country experience. We discuss our findings with respect to Gaur and Lu’s model, which explores the relationships between these variables in a general context