Full Ring Research Articles

Socle pairings on tautological rings

We study some aspects of the $\lambda_g$ pairing on the tautological ring of $M_g^c$, the moduli space of genus $g$ stable curves of compact type. We consider pairing kappa classes with pure boundary strata, all tautological classes supported on the boundary, or the full tautological ring. We prove that the rank of this restricted pairing is equal in the first two cases and has an explicit formula in terms of partitions, while in the last case the rank increases by precisely the rank of the $\lambda_g\lambda_{g - 1}$ pairing on the tautological ring of $M_g$.

Integer-valued polynomials over block matrix algebras

In this paper, we state a generalization of the ring of integer-valued polynomials over upper triangular matrix rings. The set of integer-valued polynomials over some block matrix rings is studied. In fact, we consider the set of integer-valued polynomials [Formula: see text] for each [Formula: see text], where [Formula: see text] is an integral domain with quotient field [Formula: see text] and [Formula: see text] is a block matrix ring between upper triangular matrix ring [Formula: see text] and full matrix ring [Formula: see text]. In fact, we have [Formula: see text]. It is known that the sets of integer-valued polynomials [Formula: see text] and [Formula: see text] are rings. We state some relations between the rings [Formula: see text] and the partitions of [Formula: see text]. Then, we show that the set [Formula: see text] is a ring for each [Formula: see text]. Further, it is proved that if the ring [Formula: see text] is not Noetherian then the ring [Formula: see text] is not Noetherian, too. Finally, some properties and relations are stated between the rings [Formula: see text], [Formula: see text] and [Formula: see text].

Patient-prosthesis mismatch in mitral annuloplasty for degenerative mitral regurgitation: an ignored issue.

Elevated postoperative transmitral gradient (TMG), partially induced by a small annuloplasty ring, is associated with late atrial fibrillation (AF) after mitral valve repair. Here, we aimed to provide the optimal cut-off of prosthetic ring size to reduce patient-prosthesis mismatch (PPM) after mitral annuloplasty. From 2006 to 2017, 262 patients who underwent mitral valve repair for degenerative pathologies were retrospectively studied. The relationships of body surface area (BSA)-indexed prosthetic orifice area (POAi)-postoperative TMG and POAi-late AF were tested using regression curves and receiver operating characteristic curves, respectively. The optimal cut-off of POAi predictive of late AF was used to define PPM. Baseline and follow-up data of patients with and without PPM were compared in propensity score-matched cohorts. In-hospital mortality was 0. Late AF was observed in 9.2% (24/262) patients during a median follow-up of 3.8 years. An exponential model was best fitted based on the POAi-postoperative TMG relationship (P < 0.001). Using late AF as the dependent variable, the optimal cut-off for PPM was POAi ≤2.28 cm2/m2 (c-statistic 0.71; sensitivity 0.61; specificity 0.80; P < 0.001). PPM was identified in 113 (43.1%) patients. After propensity score matching, the estimated 5-year rate of late AF was significantly higher in PPM patients than in non-PPM patients (24% vs 5%; P < 0.001). Postoperative TMG increases significantly with a small POAi for full ring annuloplasty. A patient's BSA should be considered in addition to valvular dimensions during the selection of a proper ring size to reduce PPM-related AF.

The nil Temperley–Lieb algebra of type affine C

We introduce a type affine C analogue of the nil Temperley–Lieb algebra, in terms of generators and relations. We show that this algebra T(n), which is a quotient of the positive part of a Kac–Moody algebra of type Dn+1(2), has an easily described faithful representation as an algebra of creation and annihilation operators on particle configurations, reminiscent of the open TASEP model in statistical physics. The centre of T(n) consists of polynomials in a certain element Q, and T(n) is a free module of finite rank over its centre. We show how to localize T(n) by adjoining an inverse of Q, and prove that the resulting algebra is a full matrix ring over a ring of Laurent polynomials over a field. Although T(n) has wild representation type, over an algebraically closed field we can classify all the finite dimensional indecomposable representations of T(n) in which Q acts invertibly.

Concentric ring topology of mammalian cortical sectors and relevance for patterning studies.

Models aiming to explain causally the evolutionary or ontogenetic emergence of the pallial isocortex and its regional/areal heterogeneity in mammals use simple or complex assumptions about the pallial structure present in basal mammals and nonmammals. The question arises: how complex is the pattern that needs to be accounted for in causal models? This topic is also paramount for comparative purposes, since some topological relationships may be explained as being ancestral, rather than newly emerged. The mouse pallium is apt to be reexamined in this context, due to the breadth of available molecular markers and correlative experimental patterning results. We center the present essay on a recapitulative glance at the classic theory of concentric mammalian allo-, meso-, and neocortex domains. In its simplest terms, this theory postulates a central neocortical island (6 layers) separated by a surrounding mesocortical ring (4-5 layers) from a peripheral allocortical ring (3 layers). These territories show additional partition into regional or areal subdivisions. There are also borderline amygdalar, claustral, and septal areas of the pallium, nuclear in structure. There has been little effort so far to contemplate the full concentric ring model in current "cortex patterning" models. In this essay, we recapitulate the ring idea in mammals (mouse) and consider a potential causal patterning scenario using topologic models. Finally, we briefly explore how far this theory may apply to pallium models proposed recently for sauropsids.

A Note on Cyclotomic Integers

In this note, we present a new proof that the ring is the full ring of integers in the cyclotomic field .

Study of sensitivity and resolution for full ring PET prototypes based on continuous crystals and analytical modeling of the light distribution

Sensitivity and spatial resolution are the main parameters to maximize in the performance of a PET scanner. For this purpose, detectors consisting of a combination of continuous crystals optically coupled to segmented photodetectors have been employed. With the use of continuous crystals the sensitivity is increased with respect to the pixelated crystals. In addition, spatial resolution is no longer limited to the crystal size. The main drawback is the difficulty in determining the interaction position.In this work, we present the characterization of the performance of a full ring based on cuboid continuous crystals coupled to SiPMs. To this end, we have employed the simulations developed in a previous work for our experimental detector head. Sensitivity could be further enhanced by using tapered crystals. This enhancement is obtained by increasing the solid angle coverage, reducing the wedge-shaped gaps between contiguous detectors. The performance of the scanners based on both crystal geometries was characterized following NEMA NU 4-2008 standardized protocol in order to compare them. An average sensitivity gain over the entire axial field of view of 13.63% has been obtained with tapered geometry while similar performance of the spatial resolution has been proven with both scanners. The activity at which NECR and true peak occur is smaller and the peak value is greater for tapered crystals than for cuboid crystals. Moreover, a higher degree of homogeneity was obtained in the sensitivity map due to the tighter packing of the crystals, which reduces the gaps and results in a better recovery of homogeneous regions than for the cuboid configuration. Some of the results obtained, such as spatial resolution, depend on the interaction position estimation and may vary if other method is employed.

Atomic Scale Imaging of Reversible Ring Cyclization in Graphene Nanoconstrictions.

We present an atomic level study of reversible cyclization processes in suspended nanoconstricted regions of graphene that form linear carbon chains (LCCs). Before the nanoconstricted region reaches a single linear carbon chain (SLCC), we observe that a double linear carbon chain (DLCC) structure often reverts back to a ribbon of sp2 hybridized oligoacene rings, in a process akin to the Bergman rearrangement. When the length of the DLCC system only consists of ∼5 atoms in each LCC, full recyclization occurs for all atoms present, but for longer DLCCs we find that only single sections of the chain are modified in their bonding hybridization and no full ring closure occurs along the entire DLCCs. This process is observed in real time using aberration-corrected transmission electron microscopy and simulated using density functional theory and tight binding molecular dynamics calculations. These results show that DLCCs are highly sensitive to the adsorption of local gas molecules or surface diffusion impurities and undergo structural modifications.

Induced good gradings of structural matrix rings

Our approach to structural matrix rings defines them over preordered directed graphs. A grading of a structural matrix ring is called a good grading if its standard unit matrices are homogeneous. For a group G, a G-grading set is a set of arrows with the property that any assignment of these arrows to elements of G uniquely determines an induced good grading. One of our main results is that a G-grading set exists for any transitive directed graph if G is a group of prime order. This extends a result of Kelarev. However, an example of Molli Jones shows there are directed graphs which do not have G-grading sets for any cyclic group G of even order greater than 2. Finally, we count the number of nonequivalent elementary gradings by a finite group of a full matrix ring over an arbitrary field.

Curvature development in ring rolling

Loss of circularity when creating metal ring-shaped products by ring rolling is a significant industrial issue. This paper explores the previously tacit knowledge that plastic changes in curvature - required to maintain circularity - principally occur as material passes through the roll gap. Through a series of experiments and numerical simulations on half-ring workpieces, the ‘free curvature change’ is explored for the first time, finding that the ring can ‘curl up’ - the radius reducing by as much as -39% in a single pass - unless the inner roll is much smaller than the outer roll. An analytical model of free curvature change is proposed based on force equilibrium and compatibility. Under a range of ‘normal’ operating conditions this predicted free curvature change to within 7%. In (full) ring rolling the radius of curvature must continually increase. This paper proposes that regulation of curvature is achieved through bending moments at the roll entry and exit; largest when the tool size ratio is furthest from the optimum. This hypothesis is supported by Finite Element simulations of full ring rolling, finding entry and exit moments up to a quarter of the moment for a fully plastic hinge. This work could be of direct use to process designers in choosing tool sizes and guide roll force limits and suggests new ways to use guide rolls to better maintain circularity in challenging situations.

Intermediate-term outcomes of our original multiple-knot technique using ePTFE sutures for anterior mitral leaflet prolapse.

To define the outcomes of our original simple chordal replacement technique using ePTFE sutures for mitral regurgitation. Between January, 2004 and March, 2014, 38 patients underwent mitral valve repair using our chordal replacement technique for anterior leaflet prolapse. The mitral regurgitation was caused by degenerative disease in 34 patients and infective endocarditis in 4 patients. The follow-up period was 66 ± 37months and the 5-year survival rate was 95 ± 4%. Two patients had recurrent mitral regurgitation, caused by degenerative change not associated with the procedure. The 5-year rate of freedom from recurrent mitral regurgitation was 94 ± 4%. In the late postoperative period, 15 (42%) patients had a mean pressure gradient > 5mmHg. Stepwise logistic regression analysis showed that the use of a full ring (odds ratio 8.9; 95% confidence interval 1.2-64; p = 0.031) and a 26mm annuloplasty (odds ratio 7.5; 95% confidence interval 1.1-50; p = 0.037) were significant independent risk factors for a mean pressure gradient > 5mmHg. The intermediate-term outcomes of our original chordal replacement technique were not inferior to those in previous reports, although a 26mm annuloplasty was found to be associated with a higher mitral valve gradient at rest.

Differential Inverse Power Series Rings with Quasi-Armendariz-like Condition

A generalization of semiprime rings and right p.q.-Baer rings, which we call quasi-Armendariz rings of differential inverse power series type (or simply, [Formula: see text]-quasi-Armendariz), is introduced and studied. It is shown that the [Formula: see text]-quasi-Armendariz rings are closed under direct sums, upper triangular matrix rings, full matrix rings and Morita invariance. Various classes of non-semiprime [Formula: see text]-quasi-Armendariz rings are provided, and a number of properties of this generalization are established. Some characterizations for the differential inverse power series ring [Formula: see text] to be quasi-Baer, generalized quasi-Baer, primary, nilary, reflexive, ideal-symmetric and left AIP are concluded, where δ is a derivation on the ring R. Finally, miscellaneous examples to illustrate and delimit the theory are given.

Investigation of Half-Ring Vortices Generated by Half-Submerged Thin Circular Plate Using Digital Particle Image Velocimetry Method

A half-ring vortex near the free surface interface of water can be generated by dragging a half-submerged thin circular plate in the fluid and quickly pulling it out. This results in faster moving water in front of the plate rolling over the slower water next to the plate and creating a vortex. This vortex tends to preserve its momentum which results in the vortex continually spinning and moving in the dragging direction. To investigate the ring’s motions, the Digital Particle Image Velocimetry (DPIV) method is used to study the flow of the vortex. Glitter is used as tracking particles which follow the flow of the water. The relationships between the radii of the ring and the plate as well as the dragging and vortex speeds are derived. In addition, the vortex size and speed appear not to be constant over time. It can be deduced experimentally that this half-ring vortex behaves similarly to a full vortex ring generated by the motion of a fully submerged circular plate.

Quasi-normality of idempotents on nilpotents

We study the structure of idempotents in non-Abelian rings, concerning a ring property near to the normality of idempotents on the set of nilpotents. We call a ring with such property right idempotent-quasi-normalizing on nilpotents (simply, right IQNN), and study the structure of right IQNN rings in relation with matrix rings, polynomial ring, and factor rings, by which we extend the class of right IQNN rings. It is proved that the class of IQNN rings contains the 2 by 2 full matrix rings over fields and the upper triangular matrix rings over reduced rings. It is shown that given any countable field K, there exists a semiprime IQNN algebra R over K such that the polynomial ring R[x] over R is IQNN but not NI, and the upper nilradical of R[x] is zero.

Optimized image acquisition for dopamine transporter imaging with ultra-high resolution clinical pinhole SPECT

SPECT can be used to image dopamine transporter (DaT) availability in the human striatum, e.g. for diagnosis of Parkinson’s disease (PD). As traditional SPECT provides limited resolution and sensitivity, we proposed a full ring focusing multi-pinhole SPECT system (G-SPECT-I (Beekman 2015 Eur. J. Nucl. Med. Mol. Imaging 42 S209)) which demonstrated a 2.5 mm reconstructed resolution in phantom scans. G-SPECT-I achieves data completeness in the scan region of interest by translating the patient bed with an xyz-stage and combining projections from all bed positions into image reconstruction using a scanning focus method (SFM). This paper aims to develop dedicated SFM parameters for performing a DaTscan with high effective sensitivity and appropriate sampling. To this end, the axial scanning length was restricted and transaxial bed trajectories with a reduced number of positions based on a convex hull data-completeness model were tested. Quantitative accuracy was assessed using full G-SPECT-I simulations of an Alderson phantom based on measured system matrices. For each sampling strategy, the specific binding ratio (SBR) and asymmetry index (AI) in the left and right striatum, as well as the Localized SBR (L-SBR) and the Localized AI (L-AI) in eight striatal sub-regions were calculated and compared to those of the reference scan which performs full brain oversampling using 112 bed positions. Results show that structures essential for PD diagnosis were visually and quantitatively barely affected even when using the lowest number of bed translations (i.e. 4). The maximum deviation from the reference was only 1.5%, 1.5%, 5.5% and 7.0% for the SBR, AI, L-SBR and L-AI, respectively, when 4 positions were used. Thus, it is possible to perform an accurate DaTscan with a confined axial scan region and a limited number of focused bed positions. This enables protocols for extremely fast dynamic SPECT scans with less than half-minute time frames, which can be useful for motion correction.

Topological Ring-Currents and Clar Sextets in Fully Benzenoid Hydrocarbons. II. Large Structures Containing More than 18 Rings.

In previous work, π-electron ring currents in several fully benzenoid hydrocarbons were calculated by means of the quasi-graph-theoretical, parameter-free Hückel-London-Pople-McWeeny (HLPM) method. It was found that for fully benzenoid hydrocarbons formed from fewer than about 17 rings all ring currents in full rings are larger in intensity than the ring current in benzene, while ring currents in the empty rings are smaller than the benzene value. There was an indication that this distinction might break down when larger systems are considered. Accordingly, these studies are here extended to a selection of fully benzenoid hydrocarbons containing up to 43 rings. It is still found that all full rings in all structures bear ring currents that are greater than the ring current in benzene but, in several of the larger systems, empty rings are found to bear ring currents greater than the benzene value. In the very largest structures examined, the ring currents in some of the empty rings are greater than the currents in as many as half of the symmetrically nonequivalent full rings. Despite this, because every full ring bears a ring current of intensity greater than that of any of the empty rings that are immediately adjacent to it, all of the full rings are regions of diatropic circulation; there is also strong diamagnetic circulation around the perimeters of each of the fully benzenoid systems studied. Both of these observations, based on the topological HLPM approach, are qualitatively in agreement with the predictions of sophisticated ab initio calculations, earlier performed on some of these fully benzenoid structures by Steiner et al.

Topological Ring-Currents and Clar Sextets in Fully Benzenoid Hydrocarbons I. Structures with Fewer than 18 Rings.

It is well-known that the very special family of conjugated systems described as "fully benzenoid hydrocarbons" have a unique Clar structure that causes all of their rings to be classified as either "full" or "empty". In this work, π-electron ring-currents in more than two dozen such structures are calculated by means of the quasi-graph-theoretical, parameter-free Hückel-London-Pople-McWeeny (HLPM) method. In the case of benzenoid hydrocarbons, the calculated values of such "topological" ring-currents depend on only the carbon-carbon connectivity of the system in question. It is found that, until a certain fully benzenoid hydrocarbon comprising 17 rings is examined, all ring currents in full rings are seen to be larger in intensity than the ring current in benzene, while such currents in empty rings are smaller than the benzene value. There is an indication that this distinction might break down when "giant" fully benzenoid structures are considered. These conclusions are consistent with chemical intuition, with earlier studies examining Clar aromatic sextets by means of NICS calculations, and with previous qualitative ab initio predictions of the patterns of π-electron current-flow in the fully benzenoid hydrocarbons.

Pine and larch tracheids capture seasonal variations of climatic signal at moisture-limited sites

Key messageAlthough the radial diameter and wall thickness of conifer tracheids from dry environments are climatic-sensitive across the full ring area, each cell parameter has a specific zone in a ring where its climatic response reaches the maximum.Seasonal dynamics of the timing and rate in cell production and differentiation imprint climate signals into intra-ring variations of anatomical wood structure (e.g. intra-annual density fluctuations). Despite recent methodological advances in quantitative wood anatomy, our understanding of xylem response to climate at the finest scale of intra-ring resolution is incomplete. The goal of this study is to investigate intra-ring changes of tracheid dimensions (cell radial diameter and wall thickness) controlled by moisture stress. Anatomical wood parameters of Pinus sylvestris and Larix sibirica from two drought-susceptible locations in Khakassia, South Siberia, were analysed. We found that inter-annual variation of tracheid parameters regularly exceeds the variation between radial tracheid files. This suggests that the climatic signal is recorded throughout the entire ring. However, each cell parameter has a specific zone in the ring where its climatic response reaches the maximum. The climatic response of the radial cell diameter has a temporal shift across the ring, which is particularly apparent in pine rings. The climatic response of cell wall thickness at the intra-ring scale has a more complex pattern. Our results facilitate investigation of the climate impact on tree rings at the finest intra-ring scale by quantifying the timing of climatic impact on ring structure and identifying specifically when climate impacts the formation of a particular cell.

Elevated gradient after mitral valve repair: The effect of surgical technique and relevance of postoperative atrial fibrillation

ObjectivesWe sought to investigate the effect of surgical technique in mitral valve repair on postoperative transmitral gradient (PTMG) and the relationship between PTMG and postoperative atrial fibrillation (AF). MethodsIn this retrospective study, 390 patients who underwent mitral valve repair for degenerative mitral regurgitation without AF were included. PTMG was measured using transthoracic echocardiography before patient discharge. At follow-up, occurrences of AF within 6 months of surgery (early AF) and 6 months after surgery (late AF), as well as clinical and echocardiographic data were documented and investigated. ResultsThe in-hospital mortality was 0, and the mean gradient was 3.1 ± 1.2 mm Hg before patient discharge. The risks for higher PTMG included cleft closure, edge-to-edge technique, full ring annuloplasty, and smaller indexed prosthetic size (P < .05 for all). After a median follow-up of 46 months, stable sinus rhythm was maintained in 73.1% of the overall cohort and early AF occurred in 22.7% of patients. A total of 32 patients (8.5%) had late AF, which was significantly associated with PTMG (odds ratio, 3.93; P = .004). The minimum P value approach identified a mean gradient of ≥4.5 mm Hg as the best threshold for predicting late AF (χ2 = 40.704; P < .001). ConclusionsPatients who undergo mitral valve repair for degenerative mitral insufficiency might benefit from modification of the existing leaflet repair and annuloplasty techniques to achieve a lower PTMG level, which is associated with a decreased incidence of late AF during midterm follow-up.

Stationary Computed Tomography for Space and other Resource-constrained Environments

Computed tomography (CT) is used to diagnose many emergent medical conditions, including stroke and traumatic brain injuries. Unfortunately, the size, weight, and expense of CT systems make them largely inaccessible for patients outside of major hospitals. We have designed a module containing multiple miniature x-ray sources that could allow for CT systems to be significantly lighter, smaller, and cheaper, and to operate without any moving parts. We have developed a novel photocathode-based x-ray source, created by depositing a thin film of magnesium on an electron multiplier. When illuminated by a UV LED, this photocathode emits a beam of electrons, with a beam current of up to 1 mA. The produced electrons are accelerated through a high voltage to a tungsten target. These sources are individually addressable and can be pulsed rapidly, through electronic control of the LEDs. Seven of these sources are housed together in a 17.5 degree arc within a custom vacuum manifold. A full ring of these modules could be used for CT imaging. By pulsing the sources in series, we are able to demonstrate x-ray tomosynthesis without any moving parts. With a clinical flat-panel detector, we demonstrate 3D acquisition and reconstructions of a cadaver swine lung.