Regularity of prime ideals

We answer several natural questions which arise from a recent paper of McCullough and Peeva providing counterexamples to the Eisenbud\u2013Goto Regularity Conjecture. We give counterexamples using Rees algebras, and also construct counterexamples that do not rely on the Mayr\u2013Meyer construction. Furthermore, examples of prime ideals for which the difference between the maximal degree of a minimal generator and the maximal degree of a minimal first syzygy can be made arbitrarily large are given. Using a result of Ananyan-Hochster we show that there exists an upper bound on regularity of prime ideals in terms of the multiplicity alone

A simple remark on a flat projective morphism with a Calabi-Yau fiber

If a K3 surface is a fiber of a flat projective morphisms over a connected noetherian scheme over the complex number field, then any smooth connected fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the same is true for higher dimensional Calabi-Yau fibers. We shall give an explicit negative answer to his question as well as a proof of his initial observation.Comment: 8 pages, main theorem is generalized, one more remark is added, mis-calculation and typos are corrected etc

Shapes of free resolutions over a local ring

We classify the possible shapes of minimal free resolutions over a regular local ring. This illustrates the existence of free resolutions whose Betti numbers behave in surprisingly pathological ways. We also give an asymptotic characterization of the possible shapes of minimal free resolutions over hypersurface rings. Our key new technique uses asymptotic arguments to study formal Q-Betti sequences.Comment: 14 pages, 1 figure; v2: sections have been reorganized substantially and exposition has been streamline

Durability of Response to Abrocitinib in Patients with Moderate-to-Severe Atopic Dermatitis After Treatment Discontinuation in a Phase 2b Trial

ntroduction: Multiple clinical trials showed that 12 weeks of abrocitinib monotherapy was safe and effective for the treatment of moderateto-severe atopic dermatitis (AD). The reversibility of pharmacologic activity after abrocitinib discontinuation was not described. Methods: This post hoc analysis used data from a phase 2b study to evaluate maintenance of disease control during a 4-week drug-free follow-up period in patients with moderate-tosevere AD treated with once-daily abrocitinib (200 mg/100 mg) or placebo for 12 weeks. Proportions of patients who achieved and maintained 50% or 75% improvement in Eczema Area and Severity Index (EASI-50/EASI75), an Investigator’s Global Assessment (IGA) score of 0/1, or at least a 4-point improvement in the pruritus numeric rating scale (pruritus NRS4) were determined. Biomarkers of Janus kinase inhibition and AD disease were measured in blood samples. Results: Among week 12 responders to abrocitinib 200 mg, 77.4%, 42.3%, 21.1%, and 42.9% maintained their EASI-50, EASI-75, IGA, and pruritus NRS4 response at week 16; corresponding proportions of week 12 responders maintaining response to abrocitinib 100 mg were 51.9%, 35.0%, 33.3%, and 43.5%, respectively. Four weeks after abrocitinib discontinuation, all AD biomarkers reverted towar

Decomposition of semigroup algebras

Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum of R[A]-submodules of the quotient ring of R[A]. In the case of a finite extension of positive affine semigroup rings we obtain an algorithm computing the decomposition. When R[A] is a polynomial ring over a field we explain how to compute many ring-theoretic properties of R[B] in terms of this decomposition. In particular we obtain a fast algorithm to compute the Castelnuovo-Mumford regularity of homogeneous semigroup rings. As an application we confirm the Eisenbud-Goto conjecture in a range of new cases. Our algorithms are implemented in the Macaulay2 package MonomialAlgebras.Comment: 12 pages, 2 figures, minor revisions. Package may be downloaded at http://www.math.uni-sb.de/ag/schreyer/jb/Macaulay2/MonomialAlgebras/html

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.

Neurotensin(8–13) analogs as dual NTS1 and NTS2 receptor ligands with enhanced effects on a mouse model of Parkinson's disease

: The modulatory interactions between neurotensin (NT) and the dopaminergic neurotransmitter system in the brain suggest that NT may be associated with the progression of Parkinson's disease (PD). NT exerts its neurophysiological effects by interactions with the human NT receptors type 1 (hNTS1) and 2 (hNTS2). Therefore, both receptor subtypes are promising targets for the development of novel NT-based analogs for the treatment of PD. In this study, we used a virtually guided molecular modeling approach to predict the activity of NT(8-13) analogs by investigating the docking models of ligands designed for binding to the human NTS1 and NTS2 receptors. The importance of the residues at positions 8 and/or 9 for hNTS1 and hNTS2 receptor binding affinity was experimentally confirmed by radioligand binding assays. Further in vitro ADME profiling and in vivo studies revealed that, compared to the parent peptide NT(8-13), compound 10 exhibited improved stability and BBB permeability combined with a significant enhancement of the motor function and memory in a mouse model of PD. The herein reported NTS1/NTS2 dual-specific NT(8-13) analogs represent an attractive tool for the development of therapeutic strategies against PD and potentially other CNS disorders

Super-heavy fermion material as metallic refrigerant for adiabatic demagnetization cooling

Low-temperature refrigeration is of crucial importance in fundamental research of condensed matter physics, as the investigations of fascinating quantum phenomena, such as superconductivity, superfluidity and quantum criticality, often require refrigeration down to very low temperatures. Currently, cryogenic refrigerators with $^3$He gas are widely used for cooling below 1 Kelvin. However, usage of the gas is being increasingly difficult due to the current world-wide shortage. Therefore, it is important to consider alternative methods of refrigeration. Here, we show that a new type of refrigerant, super-heavy electron metal, YbCo$_2$Zn$_{20}$, can be used for adiabatic demagnetization refrigeration, which does not require 3He gas. A number of advantages includes much better metallic thermal conductivity compared to the conventional insulating refrigerants. We also demonstrate that the cooling performance is optimized in Yb$_{1-x}$Sc$_x$Co$_2$Zn$_{20}$ by partial Sc substitution with $x\sim$0.19. The substitution induces chemical pressure which drives the materials close to a zero-field quantum critical point. This leads to an additional enhancement of the magnetocaloric effect in low fields and low temperatures enabling final temperatures well below 100 mK. Such performance has up to now been restricted to insulators. Since nearly a century the same principle of using local magnetic moments has been applied for adiabatic demagnetization cooling. This study opens new possibilities of using itinerant magnetic moments for the cryogen-free refrigeration