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

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

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

Plant Diversity Surpasses Plant Functional Groups and Plant Productivity as Driver of Soil Biota in the Long Term

One of the most significant consequences of contemporary global change is the rapid decline of biodiversity in many ecosystems. Knowledge of the consequences of biodiversity loss in terrestrial ecosystems is largely restricted to single ecosystem functions. Impacts of key plant functional groups on soil biota are considered to be more important than those of plant diversity; however, current knowledge mainly relies on short-term experiments.We studied changes in the impacts of plant diversity and presence of key functional groups on soil biota by investigating the performance of soil microorganisms and soil fauna two, four and six years after the establishment of model grasslands. The results indicate that temporal changes of plant community effects depend on the trophic affiliation of soil animals: plant diversity effects on decomposers only occurred after six years, changed little in herbivores, but occurred in predators after two years. The results suggest that plant diversity, in terms of species and functional group richness, is the most important plant community property affecting soil biota, exceeding the relevance of plant above- and belowground productivity and the presence of key plant functional groups, i.e. grasses and legumes, with the relevance of the latter decreasing in time.Plant diversity effects on biota are not only due to the presence of key plant functional groups or plant productivity highlighting the importance of diverse and high-quality plant derived resources, and supporting the validity of the singular hypothesis for soil biota. Our results demonstrate that in the long term plant diversity essentially drives the performance of soil biota questioning the paradigm that belowground communities are not affected by plant diversity and reinforcing the importance of biodiversity for ecosystem functioning

Sequencing and timing of strategic responses after industry disruption: evidence from post-deregulation competition in the U.S. railroad industry

This paper examines the sequencing and timing of firms’ strategic responses after significant industry disruption. We show that it is not the single strategic choice or response per se, but the sequencing and patterns of consecutive strategic responses that drive a firm’s adaptation and survival in the aftermath of a shift in the industry. We find that firms’ renewal efforts involved differential adaptability in finding balance at the juxtaposition of responding to demand-side pressures and choosing a path of new capability acquisition efficiently. Our study underscores the importance of taking a sequencing approach to studying strategic responses to industry disruption