Minimal Resolution Research Articles

On the configuration of the singular fibers of jet schemes of rational double points

To each variety X and a nonnegative integer m, there is a space Xm over X, called the jet scheme of X of order m, parametrizing m-th jets on X. Its fiber over a singular point of X is called a singular fiber. For a surface with a rational double point, Mourtada gave a one-to-one correspondence between the irreducible components of the singular fiber of Xm and the exceptional curves of the minimal resolution of X for In this article, for a surface X over with a singularity of An or D 4-type, we study the intersections of irreducible components of the singular fiber and construct a graph using this information. The vertices of the graph correspond to irreducible components of the singular fiber and two vertices are connected when the intersection of the corresponding components is maximal for the inclusion relation. In the case of An or D 4-type singularity, we show that this graph is isomorphic to the resolution graph for

Highly sensitive Mach-Zehnder interferometric micromagnetic field sensor based on 3D printing technology.

A two-photon 3D printed polymer magnetic sensing device based on a Mach-Zehnder interferometer (MZI) is proposed. One arm of the MZI contains a hollow cavity and two connecting open channels that can be filled with magnetic fluids (MFs) and sealed by the UV curable adhesive, forming a magneto-optical component of the interferometer. As the magnetic field changes, the refractive index (RI) of the MF changes, and the effective RI of the guiding mode of the waveguide changes accordingly, which results in a change in the phase of the MZI. The interferometric spectra can be used to evaluate the sensing sensitivity. The MZI structure with a hollow length of 40 µm is fabricated, and the microstructure is encapsulated with MF, demonstrating a highly sensitive magnetic field device. The experimental results show that the magnetic field sensitivity of the fabricated magnetic field device is -1.675nm/Oe. For a spectrometer with a resolution of 1 pm, the minimal detectable magnetic field resolution of the sensor is up to 59.7 nT with good stability.

Outcomes and longitudinal trend of traumatic cataract wound dehiscence in patients with blunt ocular injury

Longitudinal trends on traumatic cataract wound dehiscence are scant. In this study, we present the characteristics of traumatic cataract wound dehiscence using 15 years of longitudinal trend in one of the largest medical centers in Taiwan for a period when cataract surgeries were gradually shifting from extracapsular cataract extraction (ECCE) to phacoemulsification. All patients with a prior cataract surgery who suffered from blunt open globe trauma between 2001 and 2015 at a tertiary referral center in Taiwan were included. The number of cases per year; type of prior cataract surgery; visual acuity (VA); mechanism and place of injury were analyzed. The risk factors associated with final VA were investigated in patients followed up for ≥ 1 month. Seventy-six eyes of 75 patients were included and all of them were traumatic cataract wound dehiscence with a prior ECCE (65 eyes) or phacoemulsification. The most common mechanism and place of injury was fall and at home in both cataract surgical types. The mean log of the minimal angle resolution (logMAR) of final VA was 2.15 ± 0.88 (ECCE) and 1.61 ± 0.83 (phacoemulsification) (P = .026). The most significant risk factors associated with worse final VA were retinal detachment at the initial visit and low ocular trauma score (both P < .001). Long-term visual outcome of phacoemulsification wound dehiscence was better than that of ECCE wound after a blunt trauma.

Up‐conversion and temperature sensing properties of Na2GdMg2(VO4)3:Yb3+,Er3+ phosphors

AbstractIn this paper, Na2GdMg2(VO4)3:Yb3+,Er3+ phosphors were synthesized through high‐temperature solid‐state method. According to X‐ray powder diffractogram, diffuse reflection spectra, scanning electron microscopy, up‐conversion (UC) emission spectra, power‐dependent UC spectra, fluorescent lifetime curves, and temperature‐dependent emission spectra, the crystal structures, UC luminescent characteristics, and the performances of temperature sensing by using fluorescence intensity ratio technique were studied in detail. Heavy‐doped phosphors with 59% (Yb3+ and Er3+) doping content are achieved. In addition, excited by 980nm laser, three characteristic luminescence peaks of Er3+ at 525 nm (2H11/2 → 4I15/2), 550 nm (4S3/2 → 4I15/2) and 660 nm (4F9/2 → 4I15/2) emerge in the UC spectra of Er3+ single‐doped and Yb3+,Er3+ co‐doped phosphors. UC spectra are dominated by green emission and greatly enhanced UC emission over 389 times is realized by introducing Yb3+. In addition, the ratiometric techniques of thermally coupled energy levels of Er3+ (525/550 nm, 2H11/2/4S3/2 → 4I15/2) are used to achieve a wide range of temperature measurement. When the temperature is 303 K, relative sensitivity is as high as 0.976%K–1. The minimal temperature resolution is 0.3 K@303 K. All experimental results show Yb3+,Er3+ co‐doped Na2GdMg2(VO4)3 phosphors might act as optical temperature sensing materials.

The normal reduction number of two-dimensional cone-like singularities

Let $(A, \mathfrak m)$ be a normal two-dimensional local ring and $I$ an $\mathfrak m$-primary integrally closed ideal with a minimal reduction $Q$. Then we calculate the numbers: $\mathrm{nr}(I) = \min\{n \;|\; \overline{I^{n+1}} = Q\overline{I^n}\}, \quad \bar{r}(I) = \min\{n \;|\; \overline{I^{N+1}} = Q\overline{I^N}, \forall N\ge n\}$, $\mathrm{nr}(A)$, and $\bar{r}(A)$, where $\mathrm{nr}(A)$ (resp. $\bar{r}(A)$) is the maximum of $\mathrm{nr}(I)$ (resp. $\bar{r}(I)$) for all $\mathfrak m$-primary integrally closed ideals $I\subset A$. Then we have that $\bar{r}(A) \le p_g(A) + 1$, where $p_g(A)$ is the geometric genus of $A$. In this paper, we give an upper bound of $\bar{r}(A)$ when $A$ is a cone-like singularity (which has a minimal resolution whose exceptional set is a single smooth curve) and show, in particular, if $A$ is a hypersurface singularity defined by a homogeneous polynomial of degree $d$, then $\bar{r}(A)= \mathrm{nr}(\mathfrak m) = d-1$. Also we give an example of $A$ and $I$ so that $\mathrm{nr}(I) = 1$ but $\bar{r}(I)= \bar{r}(A) = p_g(A) +1=g+1$ for every integer $g \ge 2$.

Long-term prognosis of polypoidal choroidal vasculopathy with a 5-year remission after an initial combination therapy

PurposeTo investigate the visual prognosis of patients with polypoidal choroidal vasculopathy (PCV) with a 5-year remission after an initial combination therapy involving photodynamic therapy (PDT) and intravitreal ranibizumab (IVR) or aflibercept injection (IVA). MethodsMedical records of 69 consecutive patients with PCV treated with PDT with IVR/IVA were retrospectively reviewed, and 17 eyes were identified with a 5-year remission after the initial combination therapy. The eyes that did not require additional treatment during the 1st–5th year were assigned to the remission group and the eyes requiring additional treatment during the 1st–5th year were assigned to the recurrence group. ResultsDuring the 7-year follow-up, the mean logarithm of the minimal angle resolution best-corrected visual acuity (logMAR BCVA) significantly improved from 0.39±0.27 to 0.17±0.38 (p=2.9 × 10−4) in the remission group, whereas the mean logMAR BCVA was maintained throughout the follow-up period (0.58±0.27 to 0.60±0.48) in the recurrence group. In the remission group, only two (11.8%) of the 17 eyes experienced recurrence during the 5th–7th year. Comparison of baseline characteristics between the two groups revealed that a higher proportion of female (p=0.012), better baseline BCVA (p=3.1 × 10−3), and lower risk allele frequency in ARMS2 A69S (p=0.029) were observed in the remission group. ConclusionsThe combination therapy showed a favourable outcome for PCV over a 7-year follow-up, especially in the eyes without recurrence during the 1st–5th year. Physicians should be careful of recurrent exudation in the eyes without recurrence during the 1st–5th years, although the recurrence rate was low.

Resolution and tor algebra structures of grade 3 ideals defining compressed rings

Let R=k[x,y,z] be a standard graded 3-variable polynomial ring, where k denotes any field. We study grade 3 homogeneous ideals I⊆R defining compressed rings with socle k(−s)ℓ⊕k(−2s+1), where s⩾3 and ℓ⩾1 are integers. The case for ℓ=1 was previously studied in [8]; a generically minimal resolution was constructed for all such ideals. The paper [7] generalizes this resolution in the guise of (iterated) trimming complexes. In this paper, we show that all ideals of the above form are resolved by an iterated trimming complex. Moreover, we apply this machinery to construct ideals I such that R/I is a ring of Tor algebra class G(r) for some fixed r⩾2, and R/I may be chosen to have arbitrarily large type. In particular, this provides a new class of counterexamples to a conjecture of Avramov not already constructed by Christensen, Veliche, and Weyman in [5].

Y4GeO8:Er3+,Yb3+ up-conversion phosphors for optical temperature sensor based on FIR technique

Herein, we reported novel Y4GeO8:Er3+,Yb3+ phosphors elaborated via conventional solid-state reaction, and we further explored their properties as optical thermometer by using fluorescence intensity ratio (FIR) method complemented by detailed analysis on crystal structure, up-conversion luminescence and energy transfer from Yb3+ to Er3+. Upon 980 nm laser excitation, Y4GeO8:Er3+,Yb3+ phosphors present 525, 547 and 659 nm emission bands assigned to the characteristic transitions of Er3+. Furthermore, Y4GeO8:Er3+,Yb3+ samples show outstanding temperature sensing performances. To be specific, the minimal temperature resolution is 0.03 K (303 K), and the relative sensitivity of FIR can be up to 1.152%/K (303 K). Hence, Y4GeO8:Er3+,Yb3+ phosphors can be possible candidates for thermometry devices.

Up-conversion properties of Ba3Lu2Zn5O11:Yb3+,Er3+ phosphors for optical thermometer based on FIR technique

In this work, Ba3Lu2Zn5O11:Yb3+,Er3+ phosphors were successfully elaborated. The structures, morphology features and up-conversion characteristics were fully investigated through X-ray powder diffraction patterns, scanning electron microscopy and photoluminescence spectra, respectively. The optimal green emission sample Ba3Lu2Zn5O11:0.4Yb3+,0.02Er3+ was determined through up-conversion spectra excited by 980 nm. Based on power-dependent spectra and energy level schematics of Er3+ and Yb3+, the up-conversion luminescence behaviors and corresponding up-conversion mechanisms were interpreted in detail. Ba3Lu2Zn5O11:Yb3+,Er3+ phosphors show excellent temperature sensing performances based on fluorescence intensity ratio technique. The maximal relative sensitivity is 1.18 %K−1@303 K and the minimal temperature resolution is 0.26 K@303 K. More importantly, calculated temperature sensing repeatability at 333 K and 573 K is higher than 98%. All results suggest the great promise of Ba3Lu2Zn5O11:Yb3+,Er3+ phosphors as future precise thermometers.

Techniques used to assess intussusceptive angiogenesis: A systematic review.

Intussusceptive angiogenesis (IA) is an important physiological form of angiogenesis in which an existing vessel splits in two by the formation of an intraluminal tissue pillar. The presence of these intraluminal pillars form the hallmark of ongoing IA in growing vascular beds. However, their visualization is technically challenging. The goal of this systematic review was to investigate which techniques are being used to identify intraluminal pillars and to formulate important points to keep in mind when studying IA. A systematic literature search resulted in 154 evaluated articles of which the majority (65%) provided sufficient data to unambiguously demonstrate the presence of intraluminal pillars. Scanning electron microscopy imaging of vascular corrosion casts and serial sectioning of ultrathin sections are the most used techniques. New methods such as serial block face scanning electron microscopy and micro computed tomography (μCT) are gaining importance. Moreover, our results indicate that IA was studied in a variety of animals and tissues. IA is a biologically very relevant form of angiogenesis. Techniques to visualize intraluminal pillars need to have a minimal resolution of 1μm and should provide information on the 3D-nature of the pillars. Optimally, several techniques are combined to demonstrate ongoing IA.

Smoothings and rational double point adjacencies for cusp singularities

A cusp singularity is a surface singularity whose minimal resolution is a cycle of smooth rational curves meeting transversely. Cusp singularities come in naturally dual pairs. Looijenga proved in 1981 that if a cusp singularity is smoothable, the minimal resolution of the dual cusp is the anticanonical divisor of some smooth rational surface. In 1983, the second author and Miranda gave a criterion for smoothability of a cusp singularity, in terms of the existence of a K-trivial semistable model for the central fiber of such a smoothing. We study these "Type III degenerations" of rational surfaces with an anticanonical divisor--their deformations, birational geometry, and monodromy. Looijenga's original paper also gave a description of the rational double point configurations to which a cusp singularity deforms, but only in the case where the resolution of the dual cusp has cycle length 5 or less. We generalize this classification to an arbitrary cusp singularity, giving an explicit construction of a semistable simultaneous resolution of such an adjacency. The main tools of the proof are (1) formulas for the monodromy of a Type III degeneration, (2) a construction via surgeries on integral-affine surfaces of a degeneration with prescribed monodromy, (3) surjectivity of the period map for Type III central fibers, and (4) a theorem of Shepherd-Barron producing the simultaneous contraction to the adjacency of the cusp singularity.

SYMPLECTIC FILLINGS OF QUOTIENT SURFACE SINGULARITIES AND MINIMAL MODEL PROGRAM

We prove that every minimal symplectic filling of the link of a quotient surface singularity can be obtained from its minimal resolution by applying a sequence of rational blow-downs and symplectic antiflips. We present an explicit algorithm inspired by the minimal model program for complex 3-dimensional algebraic varieties.

Novel Multimodal, Multiscale Imaging System with Augmented Reality.

A novel multimodal, multiscale imaging system with augmented reality capability were developed and characterized. The system offers 3D color reflectance imaging, 3D fluorescence imaging, and augmented reality in real time. Multiscale fluorescence imaging was enabled by developing and integrating an in vivo fiber-optic microscope. Real-time ultrasound-fluorescence multimodal imaging used optically tracked fiducial markers for registration. Tomographical data are also incorporated using optically tracked fiducial markers for registration. Furthermore, we characterized system performance and registration accuracy in a benchtop setting. The multiscale fluorescence imaging facilitated assessing the functional status of tissues, extending the minimal resolution of fluorescence imaging to ~17.5 µm. The system achieved a mean of Target Registration error of less than 2 mm for registering fluorescence images to ultrasound images and MRI-based 3D model, which is within clinically acceptable range. The low latency and high frame rate of the prototype system has shown the promise of applying the reported techniques in clinically relevant settings in the future.

Long-term outcomes following primary versus secondary Boston keratoprosthesis type 1 implantation

Background/aimsTo compare long-term outcomes of primary versus secondary (postgraft failure) Boston keratoprosthesis type 1 (KPro) implantation.MethodsMedical records of patients at the Centre hospitalier de l’Université de Montréal having undergone KPro...

Support varieties for finite tensor categories: Complexity, realization, and connectedness

We advance support variety theory for finite tensor categories. First we show that the dimension of the support variety of an object equals the rate of growth of a minimal projective resolution as measured by the Frobenius-Perron dimension. Then we show that every conical subvariety of the support variety of the unit object may be realized as the support variety of an object. Finally, we show that the support variety of an indecomposable object is connected.

Multipath optical thermometry realized in CaSc2O4: Yb3+/Er3+ with high sensitivity and superior resolution

AbstractDesign and fabrication of contactless optical thermometer with rapid and accurate performance has become a research hotspot in recent years. Herein, CaSc2O4: Yb3+/Er3+ is employed as the intermediary for temperature sensing under the excitation of 980 nm, which is proven to afford an ultra‐sensitive and high‐resolution optical thermometry in multiple ways based on the fluorescence intensity ratio (FIR) technology. The optimal thermal sensing behaviors are realized by the FIR of Er3+:2H11/2 → 4I15/2 to 4S3/2 → 4I15/2 transition, which has a relative sensitivity of 1184/T2 and a minimal resolution of 0.03 K along with a maximal absolute error of 0.96 K. Besides that, the FIR between the thermally coupled Stark sublevels of Er3+:4F9/2 manifold (FIRR) as well as that of Er3+: 4I13/2 manifold (FIRN) can also provide excellent optical thermometry. The relative sensitivity of FIRR‐based and FIRN‐based optical thermometers are calculated to be 402/T2 and 366/T2, respectively, with a same minimal resolution of 0.09 K, which possess the potential to be used for biomedicine due to the inherent advantage of their operating wavelengths located in the biological window. The results demonstrate that CaSc2O4: Yb3+/Er3+ is a promising candidate for temperature sensing with multipath, high sensitivity, and superior resolution.

KSBA compactification of the moduli space of K3 surfaces with a purely non-symplectic automorphism of order four

We describe a compactification by KSBA stable pairs of the five-dimensional moduli space of K3 surfaces with a purely non-symplectic automorphism of order four and$U(2)\oplus D_4^{\oplus 2}$lattice polarization. These K3 surfaces can be realized as the minimal resolution of the double cover of$\mathbb {P}^{1}\times \mathbb {P}^{1}$branched along a specific$(4,\,4)$curve. We show that, up to a finite group action, this stable pairs compactification is isomorphic to Kirwan's partial desingularization of the GIT quotient$(\mathbb {P}^{1})^{8}{/\!/}\mathrm {SL}_2$with the symmetric linearization.

Spatial and temporal resolution of a fast-response aerodynamic pressure probe in grid-generated turbulence

The spatial and temporal resolution of a fast-response aerodynamic pressure probe (FRAP) is investigated in a benchmark flow of grid-generated turbulence. A grid with a mesh size of M=6.4 mm is tested for two different free-stream velocities, hence, resulting in Reynolds numbers of Re_M= {4300,12800}. A thorough analysis of the applicability of the underlying assumptions with regard to turbulence isotropy and homogeneity is carried out. Taylor’s frozen turbulence hypothesis is assumed for the calculation of deducible flow quantities, like the turbulent kinetic energy or the dissipation rate. Furthermore, besides the examination of statistical quantities, velocity spectra of measurements downstream of the grid are quantified. Results of a small fast-response five-hole pressure probe equipped with piezo-resistive differential pressure sensors are compared to single-wire hot-wire constant temperature anemometry data for two different wire lengths. Estimates of temporal and spatial turbulent scales (e.g., Taylor micro scale and Kolmogorov length scale) show good agreement to data in the literature but are affected by filtering effects. Especially in the energy spectra, very high bandwidth content cannot be resolved by the FRAP, which is mainly due to bandwidth limits in the temporal calibration of the FRAP and the minimal resolution of the integrated sensors.Graphic abstract

Quantification of Biventricular Myocardial Strain Using CMR Feature Tracking: Reproducibility in Small Animals.

Myocardial strain is a well-validated parameter for evaluating myocardial contraction. Cardiovascular magnetic resonance myocardial feature tracking (CMR-FT) is a novel method for the quantitative measurements of myocardial strain from routine cine acquisitions. In this study, we investigated the influence of temporal resolution on tracking accuracy of CMR-FT and the intraobserver, interobserver, and interstudy reproducibilities for biventricular strain analysis in mice from self-gated CMR at 11.7 T. 12 constitutive nexilin knockout (Nexn-KO) mice, heterozygous (Het, N = 6) and wild-type (WT, N = 6), were measured with a well-established self-gating sequence twice within two weeks. CMR-FT measures of biventricular global and segmental strain parameters were derived. Interstudy, intraobserver, and interobserver reproducibilities were investigated. For the assessment of the impact of the temporal resolution for the outcome in CMR-FT, highly oversampled semi-4 chamber and midventricular short-axis data were acquired and reconstructed with 10 to 80 phases per cardiac cycle. A generally reduced biventricular myocardial strain was observed in Nexn-KO Het mice. Excellent intraobserver and interobserver reproducibility was achieved in all global strains (ICC range from 0.76 to 0.99), where global right ventricle circumferential strain (RCSSAX) showed an only good interobserver reproducibility (ICC 0.65, 0.11-0.89). For interstudy reproducibility, left ventricle longitudinal strain (LLSLAX) was the most reproducible measure of strain (ICC 0.90, 0.71-0.97). The left ventricle radial strain (LRSSAX) (ICC 0.50, 0.10-0.83) showed fair reproducibility and RCSSAX (ICC 0.36, 0.14-0.74) showed only poor reproducibility. In general, compared with global strains, the segmental strains showed relatively lower reproducibility. A minimal temporal resolution of 20 phases per cardiac cycle appeared sufficient for CMR-FT strain analysis. The analysis of myocardial strain from high-resolution self-gated cine images by CMR-FT provides a highly reproducible method for assessing myocardial contraction in small rodent animals. Especially, global LV longitudinal and circumferential strain revealed excellent reproducibility of intra- and interobserver and interstudy measurements.

τ-Rigid Modules for Algebras with Radical Square Zero

For a radical square zero algebra [Formula: see text] and an indecomposable right [Formula: see text]-module [Formula: see text], when [Formula: see text] is Gorenstein of finite representation type or [Formula: see text] is [Formula: see text]-rigid, [Formula: see text] is [Formula: see text]-rigid if and only if the first two projective terms of a minimal projective resolution of [Formula: see text] have no non-zero direct summands in common. In particular, we determine all [Formula: see text]-tilting modules for Nakayama algebras with radical square zero.