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

On implicational bases of closure systems with unique critical sets

We show that every optimum basis of a finite closure system, in D.Maier's sense, is also right-side optimum, which is a parameter of a minimum CNF representation of a Horn Boolean function. New parameters for the size of the binary part are also established. We introduce a K-basis of a general closure system, which is a refinement of the canonical basis of Duquenne and Guigues, and discuss a polynomial algorithm to obtain it. We study closure systems with the unique criticals and some of its subclasses, where the K-basis is unique. A further refinement in the form of the E-basis is possible for closure systems without D-cycles. There is a polynomial algorithm to recognize the D-relation from a K-basis. Thus, closure systems without D-cycles can be effectively recognized. While E-basis achieves an optimum in one of its parts, the optimization of the others is an NP-complete problem.Comment: Presented on International Symposium of Artificial Intelligence and Mathematics (ISAIM-2012), Ft. Lauderdale, FL, USA Results are included into plenary talk on conference Universal Algebra and Lattice Theory, June 2012, Szeged, Hungary 29 pages and 2 figure

Neuropsychological Decline Stratifies Dementia Risk in Cognitively Unimpaired and Impaired Older Adults

ObjectiveValidation and widespread use of markers indicating decline in serial neuropsychological exams has remained elusive despite potential value in prognostic and treatment decision-making. This study aimed to operationalize neuropsychological decline, termed “neuropsychological (NP) decline,” in older adults followed over 12 months in order to aid in the stratification of dementia risk along the cognitively unimpaired-to-mild cognitive impairment (MCI) spectrum.MethodsA prospective cohort study utilized 6,794 older adults from the National Alzheimer’s Coordinating Center (NACC) database with a baseline diagnosis of normal cognition, impaired without MCI or with MCI. Operationalization of NP decline over 12-month follow-up used regression-based norms developed in a robustly normal reference sample. The extent to which each participant’s 12-month follow-up score deviated from norm-referenced expectations was quantified and standardized to an NP decline z-score. Cox regression evaluated whether the NP decline metric predicted future dementia.ResultsParticipant’s NP decline scores predicted future all-cause dementia in the total sample, χ2 = 110.71, hazard ratio (HR) = 1.989, p < 0.001, and in the subset diagnosed with normal cognition, χ2 = 40.84, HR = 2.006, p < 0.001, impaired without MCI diagnosis, χ2 = 14.89, HR = 2.465, p < 0.001, and impaired with MCI diagnosis, χ2 = 55.78, HR = 1.916, p < 0.001.ConclusionOperationalizing NP decline over 12 months with a regression-based norming method allows for further stratification of dementia risk along the cognitively unimpaired-to-MCI spectrum. The use of NP decline as an adjunctive marker of risk beyond standard cognitive diagnostic practices may aid in prognosis and clinical decision-making

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

Developmental changes associated with cross-language similarity in bilingual children

Online publication 30/9/2015The main goal of the present study was to investigate how the degree of orthographic overlap between translation equivalents influences bilingual word recognition processes at different stages of reading development. Spanish–Basque bilingual children with ages ranging from 8 to 15 years were tested in an explicit translation recognition task with a large set of items. Critically, the degree of cross-language similarity (i.e. the cognate status) between the references and the correct targets was manipulated along a continuum in order to investigate how the reliance on crosslanguage orthographic overlap varies as a function of reading experience. Results showed that younger children were significantly more sensitive to the cognate status of words than older children while recognising translation equivalents, and that this difference did not depend on the speed of response of the participants. These results demonstrate that the influence of cross-language similarity progressively diminishes as a function of increased exposure to print together with the maturation of the mechanisms responsible for language interference suppression, as suggested by developmental models of bilingual lexical access.This research has been partially funded by the Spanish Government [grant number PSI2012-32123], the European Research Council [grant number ERC-AdG-295362], and by the AThEME project funded by the European Union [grant number 613465]

Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits

The ability to generate particles from the quantum vacuum is one of the most profound consequences of Heisenberg's uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, have been used in the experimental demonstration of the dynamical Casimir effect, and may soon be able to realize the elusive verification of analogue Hawking radiation. This article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analogue, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.Comment: 27 pages, 10 figures, version published in Rev. Mod. Phys. as a Colloquiu

A Comprehensive Profile of Decoding and Comprehension in Autism Spectrum Disorders

The present study examined intake data from 384 participants with autism spectrum disorders (ASD) and a comparison group of 100 participants with dyslexia on nine standardized measures of decoding and comprehension. Although diagnostic groups were based on parental reports and could not be verified independently, we were able to observe significant distinctions between subject groups. Overall findings confirm previous results of a disassociation between decoding and comprehension in ASD. Using a larger sample than previous studies and a greater variety of measures, a pattern of relatively intact decoding skills paired with low comprehension was found in autism, PDD-NOS, and Asperger’s. In contrast, the dyslexic group showed the opposite pattern of stronger comprehension and weaker decoding

Oral Gavage Delivery of Stable Isotope Tracer for in Vivo Metabolomics

Stable isotope-resolved metabolomics (SIRM) is a powerful tool for understanding disease. Advances in SIRM techniques have improved isotopic delivery and expanded the workflow from exclusively in vitro applications to in vivo methodologies to study systemic metabolism. Here, we report a simple, minimally-invasive and cost-effective method of tracer delivery to study SIRM in vivo in laboratory mice. Following a brief fasting period, we orally administered a solution of [U-13C] glucose through a blunt gavage needle without anesthesia, at a physiological dose commonly used for glucose tolerance tests (2 g/kg bodyweight). We defined isotopic enrichment in plasma and tissue at 15, 30, 120, and 240 min post-gavage. 13C-labeled glucose peaked in plasma around 15 min post-gavage, followed by period of metabolic decay and clearance until 4 h. We demonstrate robust enrichment of a variety of central carbon metabolites in the plasma, brain and liver of C57/BL6 mice, including amino acids, neurotransmitters, and glycolytic and tricarboxylic acid (TCA) cycle intermediates. We then applied this method to study in vivo metabolism in two distinct mouse models of diseases known to involve dysregulation of glucose metabolism: Alzheimer’s disease and type II diabetes. By delivering [U-13C] glucose via oral gavage to the 5XFAD Alzheimer’s disease model and the Lepob/ob type II diabetes model, we were able to resolve significant differences in multiple central carbon pathways in both model systems, thus providing evidence of the utility of this method to study diseases with metabolic components. Together, these data clearly demonstrate the efficacy and efficiency of an oral gavage delivery method, and present a clear time course for 13C enrichment in plasma, liver and brain of mice following oral gavage of [U-13C] glucose—data we hope will aid other researchers in their own 13C-glucose metabolomics study design