scholarly journals Depth functions of symbolic powers of homogeneous ideals

2019 ◽  
Vol 218 (3) ◽  
pp. 779-827 ◽  
Author(s):  
Hop Dang Nguyen ◽  
Ngo Viet Trung
Keyword(s):  
Depth Functions ◽  
Symbolic Powers ◽  
Homogeneous Ideals

scholarly journals Correction to: Depth functions of symbolic powers of homogeneous ideals

2019 ◽  
Vol 218 (3) ◽  
pp. 829-831
Author(s):  
Hop Dang Nguyen ◽  
Ngo Viet Trung
Keyword(s):  
Depth Functions ◽  
Symbolic Powers ◽  
Homogeneous Ideals

Points fattening on and symbolic powers of bi-homogeneous ideals

2014 ◽  
Vol 218 (8) ◽  
pp. 1555-1562 ◽  
Author(s):  
Magdalena Baczyńska ◽  
Marcin Dumnicki ◽  
Agata Habura ◽  
Grzegorz Malara ◽  
Piotr Pokora ◽  
...  
Keyword(s):  
Symbolic Powers ◽  
Homogeneous Ideals

scholarly journals Depth functions of powers of homogeneous ideals

2020 ◽  
pp. 1 ◽  
Author(s):  
Huy Tài Hà ◽  
Hop Nguyen ◽  
Ngo Viet Trung ◽  
Tran Nam Trung
Keyword(s):  
Depth Functions ◽  
Homogeneous Ideals

scholarly journals Symbolic Powers of Certain Cover Ideals of Graphs

2021 ◽  
Author(s):  
Arvind Kumar ◽  
Rajiv Kumar ◽  
Rajib Sarkar ◽  
S. Selvaraja
Keyword(s):  
Symbolic Powers

scholarly journals Neural Rate and Timing Cues for Detection and Discrimination of Amplitude-Modulated Tones in the Awake Rabbit Inferior Colliculus

2007 ◽  
Vol 97 (1) ◽  
pp. 522-539 ◽  
Author(s):  
Paul C. Nelson ◽  
Laurel H. Carney
Keyword(s):  
Inferior Colliculus ◽  
Dynamic Range ◽  
Modulation Depth ◽  
Average Rate ◽  
Modulation Frequency ◽  
Detection Threshold ◽  
Depth Functions ◽  
Depth Discrimination ◽  
High Modulation ◽  
Envelope Processing

Neural responses to amplitude-modulated (AM) tones in the unanesthetized rabbit inferior colliculus (IC) were studied in an effort to establish explicit relationships between physiological and psychophysical measures of temporal envelope processing. Specifically, responses to variations in modulation depth ( m) at the cell’s best modulation frequency, with and without modulation maskers, were quantified in terms of average rate and synchronization to the envelope over the entire perceptual dynamic range of depths. Statistically significant variations in the metrics were used to define neural AM detection and discrimination thresholds. Synchrony emerged at modulation depths comparable with psychophysical AM detection sensitivities in some neurons, whereas the lowest rate-based neural thresholds could not account for psychoacoustical thresholds. The majority of rate thresholds (85%) were −10 dB or higher (in 20 log m), and 16% of the population exhibited no systematic dependence of average rate on m. Neural thresholds for AM detection did not decrease systematically at higher SPLs (as observed psychophysically): thresholds remained constant or increased with level for most cells tested at multiple sound-pressure levels (SPLs). At depths higher than the rate-based detection threshold, some rate modulation-depth functions were sufficiently steep with respect to the across-trial variability of the rate to predict depth discrimination thresholds as low as 1 dB (comparable with the psychophysics). Synchrony, on the other hand, did not vary systematically with m in many cells at high modulation depths. A simple computational model was extended to reproduce several features of the modulation frequency and depth dependence of both transient and sustained pure-tone responders.

scholarly journals A Note on the $k$-Buchsbaum Property of Symbolic Powers of Stanley-Reisner Ideals

2011 ◽  
Vol 34 (1) ◽  
pp. 221-227 ◽  
Author(s):  
Nguyên Công MINH ◽  
Yukio NAKAMURA
Keyword(s):  
Symbolic Powers

scholarly journals Stanley depth and symbolic powers of monomial ideals

2017 ◽  
Vol 120 (1) ◽  
pp. 5 ◽  
Author(s):  
S. A. Seyed Fakhari
Keyword(s):  
Monomial Ideal ◽  
Monomial Ideals ◽  
Limit Behavior ◽  
Stanley Depth ◽  
Symbolic Powers

The aim of this paper is to study the Stanley depth of symbolic powers of a squarefree monomial ideal. We prove that for every squarefree monomial ideal $I$ and every pair of integers $k, s\geq 1$, the inequalities $\mathrm{sdepth} (S/I^{(ks)}) \leq \mathrm{sdepth} (S/I^{(s)})$ and $\mathrm{sdepth}(I^{(ks)}) \leq \mathrm{sdepth} (I^{(s)})$ hold. If moreover $I$ is unmixed of height $d$, then we show that for every integer $k\geq1$, $\mathrm{sdepth}(I^{(k+d)})\leq \mathrm{sdepth}(I^{{(k)}})$ and $\mathrm{sdepth}(S/I^{(k+d)})\leq \mathrm{sdepth}(S/I^{{(k)}})$. Finally, we consider the limit behavior of the Stanley depth of symbolic powers of a squarefree monomial ideal. We also introduce a method for comparing the Stanley depth of factors of monomial ideals.

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