Iterative solutions to the steady state density matrix for optomechanical systems

We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering is efficient, adding little overhead to the computation, and results in a marked reduction in both memory and runtime requirements compared to other solution methods, with performance gains increasing with system size. Either of these benchmarks can be tuned via the preconditioner accuracy and solution tolerance. This reordering optimizes the condition number of the approximate inverse, and is the only method found to be stable at large Hilbert space dimensions. This allows for steady state solutions to otherwise intractable quantum optomechanical systems.Comment: 10 pages, 5 figure

Ordered direct implication basis of a finite closure system

Closure system on a nite set is a unifying concept in logic programming, relational data bases and knowledge systems. It can also be presented in the terms of nite lattices, and the tools of economic description of a nite lattice have long existed in lattice theory. We present this approach by describing the so-called D-basis and introducing the concept of ordered direct basis of an implicational system. A direct basis of a closure operator, or an implicational system, is a set of implications that allows one to compute the closure of an arbitrary set by a single iteration. This property is preserved by the D-basis at the cost of following a prescribed order in which implications will be attended. In particular, using an ordered direct basis allows to optimize the forward chaining procedure in logic programming that uses the Horn fragment of propositional logic. One can extract the D-basis from any direct unit basis in time polynomial in the size s( ), and it takes only linear time of the cardinality of the D-basis to put it into a proper order. We produce examples of closure systems on a 6-element set, for which the canonical basis of Duquenne and Guigues is not ordered direc

Lattices of quasi-equational theories as congruence lattices of semilattices with operators, Part I

We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+,0,F). As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found.Comment: Presented on International conference "Order, Algebra and Logics", Vanderbilt University, 12-16 June, 2007 25 pages, 2 figure

Educational attainment in poor comprehenders

To date, only one study has investigated educational attainment in poor (reading) comprehenders, providing evidence of poor performance on national UK school tests at age 11 years relative to peers (Cain & Oakhill, 2006). In the present study, we adopted a longitudinal approach, tracking attainment on such tests from 11 years to the end of compulsory schooling in the UK (age 16 years). We aimed to investigate the proposal that educational weaknesses (defined as poor performance on national assessments) might become more pronounced over time, as the curriculum places increasing demands on reading comprehension. Participants comprised 15 poor comprehenders and 15 controls; groups were matched for chronological age, nonverbal reasoning ability and decoding skill. Children were identified at age 9 years using standardised measures of nonverbal reasoning, decoding and reading comprehension. These measures, along with a measure of oral vocabulary knowledge, were repeated at age 11 years. Data on educational attainment were collected from all participants (N = 30) at age 11 and from a subgroup (n = 21) at 16 years. Compared to controls, educational attainment in poor comprehenders was lower at ages 11 and 16 years, an effect that was significant at 11 years. When poor comprehenders were compared to national performance levels, they showed significantly lower performance at both time points. Low educational attainment was not evident for all poor comprehenders. Nonetheless, our findings point to a link between reading comprehension difficulties in mid to late childhood and poor educational outcomes at ages 11 and 16 years. At these ages, pupils in the UK are making key transitions: they move from primary to secondary schools at 11, and out of compulsory schooling at 16

Relational lattices via duality

The natural join and the inner union combine in different ways tables of a relational database. Tropashko [18] observed that these two operations are the meet and join in a class of lattices-called the relational lattices- and proposed lattice theory as an alternative algebraic approach to databases. Aiming at query optimization, Litak et al. [12] initiated the study of the equational theory of these lattices. We carry on with this project, making use of the duality theory developed in [16]. The contributions of this paper are as follows. Let A be a set of column's names and D be a set of cell values; we characterize the dual space of the relational lattice R(D, A) by means of a generalized ultrametric space, whose elements are the functions from A to D, with the P (A)-valued distance being the Hamming one but lifted to subsets of A. We use the dual space to present an equational axiomatization of these lattices that reflects the combinatorial properties of these generalized ultrametric spaces: symmetry and pairwise completeness. Finally, we argue that these equations correspond to combinatorial properties of the dual spaces of lattices, in a technical sense analogous of correspondence theory in modal logic. In particular, this leads to an exact characterization of the finite lattices satisfying these equations.Comment: Coalgebraic Methods in Computer Science 2016, Apr 2016, Eindhoven, Netherland

A metapopulation model for whale-fall specialists: The largest whales are essential to prevent species extinctions

The sunken carcasses of great whales (i.e., whale falls) provide an important deep-sea habitat for more than 100 species that may be considered whale-fall specialists. Commercial whaling has reduced the abundance and size of whales, and thus whale-fall habitats, as great whales were hunted and removed from the oceans, often to near extinction. In this article, we use a metapopulation modeling approach to explore the consequences of whaling to the abundance and persistence of whale-fall habitats in the deep sea and to the potential for extinction of whale-fall specialists. Our modeling indicates that the persistence of metapopulations of whale-fall specialists is linearly related to the abundance of whales, and extremely sensitive (to the fourth power) to the mean size of whales. Thus, whaling-induced declines in the mean size of whales are likely to have been as important as declines in whale abundance to extinction pressure on whale-fall specialists. Our modeling also indicates that commercial whaling, even under proposed sustainable yield scenarios, has the potential to yield substantial extinction of whale-fall specialists. The loss of whale-fall habitat is likely to have had the greatest impact on the diversity of whale-fall specialists in areas where whales have been hunted for centuries, allowing extinctions to proceed to completion. The North Atlantic experienced dramatic declines, and even extirpation, of many whale species before the 20th century; thus, extinctions of whale-fall specialists are likely to have already occurred in this region. Whale depletions have occurred more recently in the Southern Hemisphere and across most of the North Pacific; thus, these regions may still have substantial extinction debts, and many extant whale-fall specialists may be destined for extinction if whale populations do not recover in abundance and mean size over the next few decades. Prior to the resumption of commercial whaling, or the loosening of protections to reduce incidental take, the impacts of hunting on deep-sea whale-fall ecosystems, as well as differential protection of the largest whales within and across species, should be carefully considered

Non-equilibrium Landauer Transport Model for Hawking radiation from a Black Hole

We propose that the Hawking radiation energy and entropy flow rates from a black hole can be viewed as a one-dimensional (1D), non-equilibrium Landauer transport process. Support for this viewpoint comes from previous calculations invoking conformal symmetry in the near-horizon region, which give radiation rates that are identical to those of a single 1D quantum channel connected to a thermal reservoir at the Hawking temperature. The Landauer approach shows in a direct way the particle statistics independence of the energy and entropy fluxes of a black hole radiating into vacuum, as well as one near thermal equilibrium with its environment. As an application of the Landauer approach, we show that Hawking radiation gives a net entropy production that is 50% larger than that obtained assuming standard three-dimensional emission into vacuum.Comment: 14 pages, 2 figures, published versio

Ordered direct implicational basis of a finite closure system

Closure system on a finite set is a unifying concept in logic programming, relational data bases and knowledge systems. It can also be presented in the terms of finite lattices, and the tools of economic description of a finite lattice have long existed in lattice theory. We present this approach by describing the so-called D-basis and introducing the concept of ordered direct basis of an implicational system. A direct basis of a closure operator, or an implicational system, is a set of implications that allows one to compute the closure of an arbitrary set by a single iteration. This property is preserved by the D-basis at the cost of following a prescribed order in which implications will be attended. In particular, using an ordered direct basis allows to optimize the forward chaining procedure in logic programming that uses the Horn fragment of propositional logic. One can extract the D-basis from any direct unit basis S in time polynomial in the size of S, and it takes only linear time of the cardinality of the D-basis to put it into a proper order. We produce examples of closure systems on a 6-element set, for which the canonical basis of Duquenne and Guigues is not ordered direct.Comment: 25 pages, 10 figures; presented at AMS conference, TACL-2011,ISAIM-2012 and at RUTCOR semina