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

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

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

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.

A Controversy That Has Been Tough to Swallow: Is the Treatment of Achalasia Now Digested?

Esophageal achalasia is a rare neurodegenerative disease of the esophagus and the lower esophageal sphincter that presents within a spectrum of disease severity related to progressive pathological changes, most commonly resulting in dysphagia. The pathophysiology of achalasia is still incompletely understood, but recent evidence suggests that degeneration of the postganglionic inhibitory nerves of the myenteric plexus could be due to an infectious or autoimmune mechanism, and nitric oxide is the neurotransmitter affected. Current treatment of achalasia is directed at palliation of symptoms. Therapies include pharmacological therapy, endoscopic injection of botulinum toxin, endoscopic dilation, and surgery. Until the late 1980s, endoscopic dilation was the first line of therapy. The advent of safe and effective minimally invasive surgical techniques in the early 1990s paved the way for the introduction of laparoscopic myotomy. This review will discuss the most up-to-date information regarding the pathophysiology, diagnosis, and treatment of achalasia, including a historical perspective. The laparoscopic Heller myotomy with partial fundoplication performed at an experienced center is currently the first line of therapy because it offers a low complication rate, the most durable symptom relief, and the lowest incidence of postoperative gastroesophageal reflux

Neurotensins and their therapeutic potential: Research field study

The natural tridecapeptide neurotensin has been emerged as a promising therapeutic scaffold for the treatment of neurological diseases and cancer. In this work, we aimed to identify the top 100 most cited original research papers as well as recent key studies related to neurotensins. The Web of Science Core Collection database was searched and the retrieved research articles were analyzed by using the VOSviewer software. The most cited original articles were published between 1973 and 2013. The top-cited article was by Carraway and Leeman reporting the discovery of neurotensin in 1973. The highly cited terms were associated with hypotension and angiotensin-converting-enzyme. The conducted analysis reveals the therapeutic potentials of neurotensin, and further impactful research toward its clinical development is warrantied