Shimura subvarieties in the Prym locus of ramified Galois coverings

We study Shimura (special) subvarieties in the moduli space $$A_{p,D}$$ A p , D of complex abelian varieties of dimension p and polarization type D. These subvarieties arise from families of covers compatible with a fixed group action on the base curve such that the quotient of the base curve by the group is isomorphic to $${{\mathbb {P}}}^1$$ P 1 . We give a criterion for the image of these families under the Prym map to be a special subvariety and, using computer algebra, obtain 210 Shimura subvarieties contained in the Prym locus.

Shimura curves in the Prym loci of ramified double covers

We study Shimura curves of PEL type in the space of polarized abelian varieties [Formula: see text] generically contained in the ramified Prym locus. We generalize to ramified double covers, the construction done in [E. Colombo, P. Frediani, A. Ghigi and M. Penegini, Shimura curves in the Prym locus, Commun. Contemp. Math. 21(2) (2019) 1850009] in the unramified case and in the case of two ramification points. Namely, we construct families of double covers which are compatible with a fixed group action on the base curve. We only consider the case of one-dimensional families and where the quotient of the base curve by the group is [Formula: see text]. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci.

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.

Speech performance in adult patients undergoing Invisalign treatment:

ABSTRACT Objectives To assess speech performance of adult patients undergoing orthodontic treatment with Invisalign. Materials and Methods Twenty-four adult patients with Invisalign (Invisalign group: 6 men, 18 women; average age; 34.88 years) and 20 adult patients with fixed labial appliances (fixed group: 5 men, 15 women; average age; 38.85 years) were evaluated. Speech was recorded immediately before delivery of the first set of clear aligners or bonding of labial appliances (T0), immediately after delivery or bonding (T1), and 2 months after delivery or bonding (T2). Speech was evaluated via a combination of three auditory analyses: (1) objective acoustic analysis through digital sonography, (2) semiobjective assessment by six speech and language pathologists, and (3) subjective assessment patient questionnaire. Results The objective acoustic analysis showed a statistically significant difference over time from T0 to T1, T1 to T2, and T0 to T2 for Invisalign patients. The semiobjective analysis revealed a significant speech alteration from T0 to T1 and T1 to T2 for both groups, and from T0 to T2 in the Invisalign group. The subjective analysis showed a significant difference between means of Invisalign and fixed group patient perception at both T1 and T2. Conclusions Invisalign treatment significantly affected speech, and although patients experience some level of adaptation, speech does not return to normal after 2 months of treatment.

Feasibility and efficacy of modified fixed citrate concentration protocol using only commercial preparations in critically ill patients: a prospective cohort study with a historical control group

Background The cumbersome program and the shortage of commercial solution hindered the regular application of regional citrate anticoagulation (RCA). It is urgent to simplify the protocol using only commercial preparations. The aim of this study was to explore the feasibility and efficacy of the modified protocol for continuous veno-venous hemofiltration (CVVH) in unselected critically ill patients. Methods A prospective cohort study was conducted in 66 patients who received a new protocol combining fixed citrate concentration with modified algorithm for supplements (i.e., fixed protocol), and compared the efficacy, safety and convenience for this group to a historical control group with a traditional protocol (n = 64), where citrate was titrated according to the circuit ionized calcium concentration (i.e., titrated protocol). The convenience was defined as the demand for monitoring test and dose adjustment of any supplement. Results The filter lifespan was 63.2 ± 16.1 h in the fixed group and 51.9 ± 17.7 h in the titrated group, respectively. Kaplan-Meier survival analysis demonstrated longer circuit lifetime for fixed group (log-rank, p = 0.026). The incidence of circuit clotting was lower in the fixed protocol (15.2% vs. 29.7% in the titrated protocol, p = 0.047). Moreover, compared with the titrated group, patients with fixed protocol had less demand for monitoring test and dose adjustment of any supplement (the number of times per person per day) (3.3 [IQR 2.3–4.5] vs. 5.7 [IQR 3.3–6.9], p = 0.001 and 1.9 [IQR 0.5–2.7] vs. 6.3 [IQR 4.2–7.9], p < 0.001; respectively). No new onset bleeding complications occurred in all patients. The overall incidence of suspected citrate accumulation was 4.6% and there was no difference between the two groups (p = 0.969), yet a lower rate of metabolic alkalosis was found in the fixed group (3.0% vs. 14.1%, p = 0.024). Conclusions Our modified fixed citrate concentration protocol is feasible, safe and effective to enhance the circuit lifespan and the convenience of implementation while maintaining a similar safety when compared to the traditional protocol. Using only commercial preparations may be helpful for widespread application of RCA. Trial registration Clinicaltrials.gov. NCT02663960. Registered 26 January 2016.

Deuterocanonical and Apocryphal Books

The terms ‘deuterocanonical’ (a later, Catholic, term) or ‘apocryphal’ (used by early Church writers) are popularly used to refer to religious books from the Judeo-Christian tradition perceived as having a lower status than those books regarded as normative for doctrine. Both ‘deuterocanonical’ and ‘apocryphal’ imply the recognition of a contrasting fixed group of authoritative scriptural works, with which the ‘deuterocanonical’ and ‘apocryphal’ books are associated. This chapter focuses on books transmitted in early Greek Christian pandect Bibles and associated with the LXX corpus, but whose status was debated within Christian circles and largely unrecognized by rabbinic Judaism. It explores the original language, date, Greek text form, and witnesses to those complete books most commonly listed in modern times as deuterocanonical, along with some semi-independent works including the Letter of Jeremiah, the Prayer of Manasseh, and Psalm 151. (The additions to Esther, Daniel, and Jeremiah are covered in Chapters 18, 20, and 22 in this volume, on Jeremiah, Daniel, and the Megillot respectively.)

Comparison of pain perception, anxiety, and impacts on oral health-related quality of life between patients receiving clear aligners and fixed appliances during the initial stage of orthodontic treatment

Background and Objectives Clear aligner is an advanced orthodontic method with benefits of comfort, aesthetics, and convenience. This study aimed to compare pain perception, anxiety, and impacts on oral health-related quality of life (OHRQoL) between adult patients receiving clear aligners and fixed appliances during the initial stage of orthodontic treatments. Material and Methods The two groups were well matched by ages, gender, and levels of malocclusion severity. Pain perception, anxiety, and OHRQoL were assessed through visual analogue scale, state-trait anxiety inventory, and oral health impact profile-14 (OHIP-14), respectively. And the comparison of above scores was performed by two-way analysis of variance. Results A total of 110 patients (55 pairs) were enrolled in this study. Orthodontic pain levels peaked on the first day and decreased gradually afterwards in both groups, which were significantly higher in the fixed group on the first, second, fourth, and fifth days. Likewise, anxiety levels peaked on the first day and decreased thereafter, with significant difference on the 1st, 3d, 5th, 7th, and 14th days. Moreover, the OHIP-14 scores increased and peaked on the first day and then gradually decreased for both groups, which were also significantly higher in the fixed group on the 1st, 7th, and 14th days. Limitations More malocclusion types should be used for group matching. The effect of exclusion of small groups should be taken into consideration in sample size calculation. Income was significantly unbalanced between two groups due to higher cost of clear aligners, and random assignment of treatment modalities was unfeasible. Conclusions Patients treated with clear aligners experienced lower pain levels, less anxiety, and higher OHRQoL as compared to those receiving fixed appliances.

Homological Stability for Spaces of Commuting Elements in Lie Groups

In this paper, we study homological stability for spaces $\textrm{Hom}({{\mathbb{Z}}}^n,G)$ of pairwise commuting $n$-tuples in a Lie group $G$. We prove that for each $n\geqslant 1$, these spaces satisfy rational homological stability as $G$ ranges through any of the classical sequences of compact, connected Lie groups, or their complexifications. We prove similar results for rational equivariant homology, for character varieties, and for the infinite-dimensional analogues of these spaces, $\textrm{Comm}(G)$ and $B_{\textrm{com}} G$, introduced by Cohen–Stafa and Adem–Cohen–Torres-Giese, respectively. In addition, we show that the rational homology of the space of unordered commuting $n$-tuples in a fixed group $G$ stabilizes as $n$ increases. Our proofs use the theory of representation stability—in particular, the theory of $\textrm{FI}_W$-modules developed by Church–Ellenberg–Farb and Wilson. In all of the these results, we obtain specific bounds on the stable range, and we show that the homology isomorphisms are induced by maps of spaces.

Quantification of pterygium fibroconnective components utilizing freeze-dried method

Introduction: To propose an objective method of quantifying pterygium fibroconnective components utilizing freeze-dried method. Methods: 60 primary pterygium were excised using controlled partial avulsion technique performed by a single surgeon (KMK), and divided into two groups: formalin-fixed (n=30) and fresh (n=30). Initially, each sterile container weight was measured and 5ml of 5% buffered formaldehyde were filled and stored for 1 week for formalin-fixed group while, 5ml distilled water were filled for fresh pterygium group. Each container was pre-frozen for 12 hours prior to freeze-dried (-80ºC for 24 hours). The final product known as fibroconnective tissue, then weighted as dry weight. Comparative analysis of wet and dry weight, and percentage of fibroconnective components between groups were performed via an independent t-test. Results: The overall mean and SD for formalin-fixed and fresh pterygium wet weight were 253.33 ± 82.17 μg and 255.17 ± 63.52 μg, and dry weight were 184.92 ± 84.31 μg and 179.54 ± 72.85 μg respectively. In terms of percentage of fibroconnective components, formalin-fixed group revealed slightly higher percentage compared to fresh pterygium tissue with 69.39 ± 13.29 % and 67.75 ± 13.27 % respectively. The difference in pterygium dry weight, between formalin-fixed and fresh pterygium tissue was statistically insignificant (p=0.792). Conclusions: The freeze-dried method can be used to quantify the fibroconnective component (dry weight) of pterygium fibro vascular tissue. Both methods (formalin-fixed and freeze-dried) are reliable in producing results. This is proven as there is no statistical significance between the two methods.

Centralized Maintenance Time Prediction Algorithm for Freight Train Wheels Based on Remaining Useful Life Prediction

Many freight trains for special lines have in common the characteristics of a fixed group. Centralized Condition-Based Maintenance (CCBM) of key components, on the same freight train, can reduce maintenance costs and enhance transportation efficiency. To this end, an optimization algorithm based on the nonlinear Wiener process is proposed, for the prediction of the train wheels Remaining Useful Life (RUL) and the centralized maintenance timing. First, Hodrick–Prescott (HP) filtering algorithm is employed to process the raw monitoring data of wheel tread wear, extracting its trend components. Then, a nonlinear Wiener process model is constructed. Model parameters are calculated with a maximum likelihood estimation and the general deterioration parameters of wheel tread wear are obtained. Then, the updating algorithm for the drift coefficient is deduced using Bayesian formula. The online updating of the model is realized, based on individual wheel monitoring data, while a probability density function of individual wheel RUL is obtained. A prediction method of RUL for centralized maintenance is proposed, based on two set thresholds: “maintenance limit” and “the ratio of limit-arriving.” Meanwhile, a CCBM timing prediction algorithm is proposed, based on the expectation distribution of individual wheel RUL. Finally, the model is validated using a 500-day online monitoring data on a fixed group, consisting of 54 freight train cars. The validation result shows that the model can predict the wheels RUL of the train for CCBM. The proposed method can be used to predict the maintenance timing when there is a large number of components under the same working conditions and following the same path of degradation.