COMPRESSION BASES IN EFFECT ALGEBRAS

Effect algebras are the main object of study in quantum mechanics. Module measures are those measures defined on an effect algebra with values on a topological module. Let R be a topological ring and M a topological R-module. Let L be an effect algebra. The range of a module measure μ:L→M is studied. Among other results, we prove that if L is an sRDP σ-effect algebra with a natural basis and μ:L→R is a countably additive measure, then μ has bounded variation.

The aim of this paper is to present several techniques of constructing a lattice-ordered effect algebra from a given family of lattice-ordered effect algebras, and to study the structure of finite lattice-ordered effect algebras. Firstly, we prove that any finite MV-effect algebra can be obtained by substituting the atoms of some Boolean algebra by linear MV-effect algebras. Then some conditions which can guarantee that the pasting of a family of effect algebras is an effect algebra are provided. At last, we prove that any finite lattice-ordered effect algebra E without atoms of type 2 can be obtained by substituting the atoms of some orthomodular lattice by linear MV-effect algebras. Furthermore, we give a way how to paste a lattice-ordered effect algebra from the family of MV-effect algebras.

Fuzzy set representations of some quantum structures

An effect algebra is a partial algebraic structure, originally formulated as an algebraic base for unsharp quantum measurements. In this article we present an approach to the study of lattice effect algebras (LEAs) that emphasizes their structure as algebraic models for the semantics of (possibly) non-standard symbolic logics. This is accomplished by focusing on the interplay among conjunction, implication, and negation connectives on LEAs, where the conjunction and implication connectives are related by a residuation law. Special cases of LEAs are MV-algebras and orthomodular lattices. The main result of the paper is a characterization of LEAs in terms of so-called Sasaki algebras. Also, we compare and contrast LEAs, Hajek's BL-algebras, and the basic algebras of Chajda, Halas, and Kuhr.

Spectral automorphisms have been introduced in [IVANOV, A.—CARAGHEORGHEOPOL, D.: Spectral automorphisms in quantum logics, Internat. J. Theoret. Phys. 49 (2010), 3146–3152]_in an attempt to construct, in the abstract framework of orthomodular lattices, an analogue of the spectral theory in Hilbert spaces. We generalize spectral automorphisms to the framework of effect algebras with compression bases and study their properties. Characterizations of spectral automorphisms as well as necessary conditions for an automorphism to be spectral are given. An example of a spectral automorphism on the standard effect algebra of a finite-dimensional Hilbert space is discussed and the consequences of spectrality of an automorphism for the unitary Hilbert space operator that generates it are shown. The last section is devoted to spectral families of automorphisms and their properties, culminating with the formulation and proof of a Stone type theorem (in the sense of Stone’s theorem on strongly continuous one-parameter unitary groups — see, e.g. [REED, M.#x2014;SIMON, B.: Methods of Modern Mathematical Physics, Vol. I, Acad. Press, New York, 1975]) for a group of spectral automorphisms.

Unified (r, s)-Entropies of Partitions on Sequential Effect Algebras

A synaptic algebra is both a special Jordan algebra and a spectral order-unit normed space satisfying certain natural conditions suggested by the partially ordered Jordan algebra of bounded Hermitian operators on a Hilbert space. The adjective “synaptic”, borrowed from biology, is meant to suggest that such an algebra coherently “ties together” the notions of a Jordan algebra, a spectral order-unit normed space, a convex effect algebra, and an orthomodular lattice.

In the orthodox quantum logic approach to foundations of quantum mechanics originated by Birkhoff and von Neumann [1] the object called quantum logic is not a logic in the very sense of this word but an algebraic structure: orthomodular lattice or poset. These orthomodular structures, abstracted from structures of Hilbert spaces used to describe quantum phenomena are weakenings of Boolean algebras. They can be thought of as representing Lindenbaum algebras of systems of propositions about quantum objects, the propositions belonging to the quantum logic proper. Since Lindenbaum algebras of propositional systems which obey the rules of classical logic are Boolean algebras it is inferred that the quantum logic proper, whatever it means, is non-classical.

Orthomodular lattices and posets, orthoalgebras, and D-posets are all examples of partial Abelian semigroups. So, too, are the event structures of test spaces. The passage from an algebraic test space to its logic (an orthoalgebra) is an instance of a general construction involving a partial Abelian semigroupL and a distinguished subsetM\( \subseteq \)L such that perspectivity with respect toM is a congruence onL. The quotient ofL by such a congruence is always a cancellative, unital PAS, and every such PAS arises canonically as such a quotient.

Pasting of lattice-ordered effect algebras

We consider the amalgamation of bounded involution posets over a strictly directed graph as applied to orthomodular lattices, orthomodular posets or orthoalgebras. In the finite setting, we show that the order dimension of the amalgamation does not exceed that of the amalgamated structures by more than one. We also present conditions under which equality obtains.

BackgroundSpinal anesthesia (SA) is a standard technique for cesarean section. Hypotension presents an incident of 80–85% after SA in pregnant women.ObjectiveTo determine the effect of intermittent pneumatic compression of lower limbs on declining spinal anesthesia induced hypotension during cesarean section.MethodsThis double-blind clinical prospective study was conducted on 76 non-laboring parturient patients, aged 18–45 years, with the American Society of Anesthesiologist physical status I or II who were scheduled for elective cesarean section at Razi Hospital, Ahvaz, Iran from December 21, 2015 to January 20, 2016. Patients were divided into treatment mechanical pump (Group M) or control group (Group C) with simple random sampling. Fetal presentation, birth weight, Apgar at 1 and 5 min, time taken for pre-hydration (min), pre-hydration to the administration of spinal anesthesia (min), initiation of spinal to the delivery (min) and total volume of intravenous fluids, total dose of ephedrine and metoclopramide were recorded. Data were analyzed by SPSS version 19, using repeated measures of ANOVA and Chi square test.ResultsHeart rate, MPA, DAP and SAP changes were significantly higher in off-pump group in the baseline and 1st-minute (p<0.05), and in the other times, this change was significantly different with control groups.ConclusionThis research showed the suitability of the use of Sequential Compression Device (SCD) in reducing hypotension after spinal anesthesia for cesarean section, also this method can cause reducing vasopressor dosage for increased blood pressure, but the approval of its effectiveness requires repetition of the study with a larger sample size.Trial registrationThe trial was registered at the Iranian Registry of Clinical Trials (http://www.irct.ir) with the IRCT ID: IRCT2015011217742N3.FundingThe authors received no financial support for the research, authorship, and/or publication of this article.

Intradural spinal cord compression impairs perfusion pressure and is putatively rate-limiting for recovery after traumatic spinal cord injury (tSCI). After cervical tSCI, even minimally improved tissue preservation may help promote neurological recovery. To assess the nature and extent of spinal cord swelling and compression post-acute cervical tSCI, we evaluated several baseline MRI parameters including BASIC score, intramedullary lesion (IML) length, maximal canal compromise (MCC), maximal spinal cord compression (MSCC), extent of cord compression (ECC), maximal swollen anteroposterior diameter adjacent to injury site (Dmax), and maximal cord swelling (MCS) in 169 consecutive patients across 2 centers. In patients with either primarily intradural or combined (MSCC ≤5% or >5%, respectively) cord compression, we examined the predictive value of clinical and imaging admission parameters on American Spinal Injury Association Impairment Scale (AIS) severity and conversion up to 1-year follow-up. 37 (21.9%) patients presented with primarily intradural while 132 (78.1%) had combined cord compression. MSCC, MCS, and Dmax values differed significantly between the two groups (p < 0.0001, < 0.01 and < 0.001, respectively). MSCC was associated with age, MCC and MCS at baseline, while MCS was associated with age, MSCC and Dmax, on multivariable analysis. Logistic regression analysis of areas under receiver operating characteristic curve (AUROC) confirmed ECC (AUC 0.678) and MCS (AUC 0.922) as good and excellent predictors, respectively of AIS-conversion at 1-year for intradural compression participants. Additionally, MCS was significantly more accurate in predicting AIS-conversion in intradural group and the probability of AIS-conversion significantly decreased with each 1% increase in MCS (p = 0.003; OR 0.949), for both compression subtypes. In conclusion, baseline measures of cord swelling predict AIS-conversion likelihood up to 1-year. The deleterious effects of intradural cord compression, either isolated or presenting with extradural compression, may benefit from supplemental decompression strategies in addition to current standard-of-care.

With widespread use of screening digital mammography, efficient storage of the vast amounts of data has become a challenge. While lossless image compression causes no risk to the interpretation of the data, it does not allow for high compression rates. Lossy compression and the associated higher compression ratios are therefore more desirable. The U.S. Food and Drug Administration (FDA) currently interprets the Mammography Quality Standards Act as prohibiting lossy compression of digital mammograms for primary image interpretation, image retention, or transfer to the patient or her designated recipient. Previous work has used reader studies to determine proper usage criteria for evaluating lossy image compression in mammography, and utilized different measures and metrics to characterize medical image quality. The drawback of such studies is that they rely on a threshold on compression ratio as the fundamental criterion for preserving the quality of images. However, compression ratio is not a useful indicator of image quality. On the other hand, many objective image quality metrics (IQMs) have shown excellent performance for natural image content for consumer electronic applications. In this paper, we create a new synthetic mammogram database with several unique features. We compare and characterize the impact of image compression on several clinically relevant image attributes such as perceived contrast and mass appearance for different kinds of masses. We plan to use this database to develop a new objective IQM for measuring the quality of compressed mammographic images to help determine the allowed maximum compression for different kinds of breasts and masses in terms of visual and diagnostic quality.

The aim: To determine the effect of compression on the venous and arterial velocity of the main blood flow of the lower limb and the skin microcirculation of the rear part of the foot. Materials and methods: 20 healthy subjects participated in this study: 11 men 11 (55%) men and 9 (45%) girls. The ankle brachial index (ABI), femoropop¬liteal index, femoral arterial blood flow velocity (AFV), venous blood flow velocity (VFV), transcutaneous oxygen pressure (tcPO2) and carbon dioxide pressure (tcPCO2) were measured. After the general measurements were taken, the tire was inflated to 10 mm Hg under general basic conditions and kept for three minutes. The experiment ended when no decrease in tcPO2 was observed between two consecutive pressure levels. Results: The average tire pressure to reach physiological zero was 80 mm Hg. for all participants. At 10 mmHg significant changes in indicators were found by 19% (p=0.0001). tcPCO2 values increased significantly at 10 mmHg (p=0.0319) and continued to increase until the end of the study. It was established that its values increased by 14% compared to the input data (p=0.0005). Conclusions: At the maximum compression of 60 mmHg the arterial blood flow rate decreased by 5.5 times (p=0.0001). TcPCO2 increases significantly when compressed by 10 mm Hg also in parallel with the decrease in the regional perfusion index, which begins at an external compression of 40 mm Hg, which is evidence of the deterioration of the perfusion of the skin of the anterior part of the foot in healthy subjects.