How to compute the Hilbert depth of a graded ideal

We give two algorithms for computing the Hilbert depth of a \emph{graded ideal} in the polynomial ring. These algorithms work efficiently for (squarefree) lex ideals. As a consequence, we construct counterexamples to some conjectures made by Shen in \cite{B:Sh2}.Comment: In this new version, we have added some materials about comparing Algorithm 2.16 to Popescu's algorithm and Bruns et al's algorith

Galectin-3 regulates intracellular trafficking of EGFR through Alix and promotes keratinocyte migration.

The EGFR-mediated signaling pathways are important in a variety of cellular processes, including cell migration and wound re-epithelialization. Intracellular trafficking of EGFR is critical for maintaining EGFR surface expression. Galectin-3, a member of an animal lectin family, has been implicated in a number of physiological and pathological processes. Through studies of galectin-3-deficient mice and cells isolated from these mice, we demonstrated that the absence of galectin-3 impairs keratinocyte migration and skin wound re-epithelialization. We have linked this pro-migratory function to a crucial role of cytosolic galectin-3 in controlling intracellular trafficking and cell surface expression of EGFR after EGF stimulation. Without galectin-3, the surface levels of EGFR are markedly reduced, and the receptor accumulates diffusely in the cytoplasm. This is associated with reduced rates of both endocytosis and recycling of the receptor. We have provided evidence that this previously unreported function of galectin-3 may be mediated through interaction with its binding partner Alix, which is a protein component of the ESCRT (endosomal sorting complex required for transport) machinery. Our results suggest that galectin-3 is potentially a critical regulator of a number of important cellular responses through its intracellular control of trafficking of cell surface receptors

Cigarette smoking and its impact on the survival outcomes and molecular features of metastatic colorectal cancer patients

https://openworks.mdanderson.org/sumexp22/1130/thumbnail.jp

Hilbert Functions And Free Resolutions

Hilbert functions and free resolutions are central concepts in the field of Commutative Algebra. In chapter 3 we prove some cases of the well-known Eisenbud-Green-Harris Conjecture. This conjecture characterizes the Hilbert functions of graded ideals containing a regular sequence in the polynomial ring. In chapter 4 we study the Hilbert functions of graded ideals in toric rings. We prove that Macaulay's Theorem holds for some projective monomial curves, and show that Macaulay's Theorem does not hold for all projective monomial curves. In the last chapter we construct explicitly the minimal free resolutions of linear edge ideals

Hilbert Functions And Free Resolutions

Hilbert functions and free resolutions are central concepts in the field of Commutative Algebra. In chapter 3 we prove some cases of the well-known Eisenbud-Green-Harris Conjecture. This conjecture characterizes the Hilbert functions of graded ideals containing a regular sequence in the polynomial ring. In chapter 4 we study the Hilbert functions of graded ideals in toric rings. We prove that Macaulay's Theorem holds for some projective monomial curves, and show that Macaulay's Theorem does not hold for all projective monomial curves. In the last chapter we construct explicitly the minimal free resolutions of linear edge ideals

Pressure-induced one-dimensional oxygen ion diffusion channel in lead-apatite

Recently, Lee et al. claimed that the experimental observation of room-temperature ambient-pressure superconductivity in a Cu-doped lead-apatite (Pb10-xCux(PO4)6O). The study revealed the Cu doping induces a chemical pressure, resulting in a structural contraction of one-dimensional Cu-O-Cu atomic column. This unique structure promotes a one-dimensional electronic conduction channel along the c-axis mediated by the O atoms, which may be related to superconductivity. These O atoms occupy 1/4 of the equivalent positions along the c-axis and exhibit a low diffusion activation energy of 0.8 eV, indicating the possibility of diffusion between these equivalent positions. Here, using machine-learning based deep potential, we predict the pressure-induced fast diffusion of 1/4-occupied O atoms along the one-dimensional channel in Pb10(PO4)6O at 500 K, while the frameworks of Pb triangles and PO4 tetrahedrons remain stable. The calculation results also indicate Cu doping can provide appropriate effective chemical pressure, indicating the one-dimensional ion diffusion channel may appear in Pb9Cu(PO4)6O, even at ambient pressure. Our finding shows that the one-dimensional ions diffusion channel may be an important factor to affects the fabrication and electrical measurement of doped lead-apatite.Comment: 15 pages, 7 figure

Multilevel Nitrogen Additions Alter Chemical Composition and Turnover of the Labile Fraction Soil Organic Matter via Effects on Vegetation and Microorganisms

Global nitrogen (N) deposition greatly impacts soil carbon sequestration. A 2- yr multiple N addition (0, 10, 20, 40, 80, and 160 kg N·ha- 1·yr- 1) experiment was conducted in alpine grassland to illustrate the mechanisms underlying the observed soil organic matter (SOM) dynamics on the Qinghai- Tibet Plateau (QTP). Labile fraction SOM (LF- SOM) fingerprints were characterized by pyrolysis- gas chromatography/tandem- mass spectrometry, and microbial functional genes (GeoChip 4.6) were analyzed in conjunction with LF- SOM fingerprints to decipher the responses of LF- SOM transformation to N additions. The significant correlations between LF- SOM and microbial biomass, between organic compounds in LF- SOM and compound degradation- related genes, and between LF- SOM and net ecosystem exchange implied LF- SOM were the main fraction utilized by microorganisms and the most sensitive fraction to N additions. The LF- SOM increased at the lowest N addition levels (10 and 20 kg N·ha- 1·yr- 1) and decreased at higher N addition levels (40 to 160 kg N·ha- 1·yr- 1), but the decrease of LF- SOM was weakened at 160 kg N·ha- 1·yr- 1 addition. The nonlinear response of LF- SOM to N additions was due to the mass balance between plant inputs and microbial degradation. Plant- derived compounds in LF- SOM were more sensitive to N addition than microbial- derived and aromatic compounds. It is predicted that when the N deposition rate increased by 10 kg N·ha- 1·yr- 1 on the QTP, carbon sequestration in the labile fraction may increase by nearly 170% compared with that under the current N deposition rate. These findings provide insight into future N deposition impacts on LF- SOM preservation on the QTP.Key PointsThe LF- SOM quantity increased at the lowest N additions (N10 and N20) and decreased from N40 to N160, but the decrease was weakened at the highest N addition (N160)Plant- derived compounds in LF- SOM were more sensitive to N addition than microbial- derived and aromatic compoundsThe organic compounds in LF- SOM were significantly correlated with compound degradation- related genesPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154963/1/jgrg21637_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154963/2/jgrg21637.pd

Methological quality of systematic reviews and meta-analyses on acupuncture for stroke: a review of review

Objective: To assess the methodological quality of systematic reviews and meta-analyses regarding acupuncture intervention for stroke and the primary studies within them. Methods: Two researchers searched PubMed, Cumulative index to Nursing and Allied Health Literature, Embase, ISI Web of Knowledge, Cochrane, Allied and Complementary Medicine, Ovid Medline, Chinese Biomedical Literature Database, China National Knowledge Infrastructure, Wanfang and Traditional Chinese Medical Database to identify systematic reviews and meta-analyses about acupuncture for stroke published from the inception to December 2016. Review characteristics and the criteria for assessing the primary studies within reviews were extracted. The methodological quality of the reviews was assessed using adapted Oxman and Guyatt Scale. The methodological quality of primary studies was also assessed. Results: Thirty-two eligible reviews were identified, 15 in English and 17 in Chinese. The English reviews were scored higher than the Chinese reviews (P=0.025), especially in criteria for avoiding bias and the scope of search. All reviews used the quality criteria to evaluate the methodological quality of primary studies, but some criteria were not comprehensive. The primary studies, in particular the Chinese reviews, had problems with randomization, allocation concealment, blinding, dropouts and withdrawals, intent-to-treat analysis and adverse events. Conclusions: Important methodological flaws were found in Chinese systematic reviews and primary studies. It was necessary to improve the methodological quality and reporting quality of both the systematic reviews published in China and primary studies on acupuncture for stroke