Hilbert functions and Jordan type of Perazzo Artinian algebras

We study Hilbert functions, Lefschetz properties, and Jordan type of Artinian Gorenstein algebras associated to Perazzo hypersurfaces in projective space. The main focus lies on Perazzo threefolds, for which we prove that the Hilbert functions are always unimodal. Further we prove that the Hilbert function determines whether the algebra is weak Lefschetz, and we characterize those Hilbert functions for which the weak Lefschetz property holds. By example, we verify that the Hilbert functions of Perazzo fourfolds are not always unimodal. In the particular case of Perazzo threefolds with the smallest possible Hilbert function, we give a description of the possible Jordan types for multiplication by any linear form.Comment: 23 page

What\u27s Next: Into a Third Decade of LatCrit Theory, Community, and Praxis

In this multi-vocal Afterword, we reflect-personally and collectively to help chart renewed agendas toward and through a third decade of LatCrit theory, community, and praxis. This personal collective exercise illustrates and reconsiders the functions, guideposts, values, and postulates for our shared programmatic work a framework for our daily work as individuals and teams through our portfolio of projects, which in turn emerged as a reflection and projection of LatCrit theory, community and praxis. These early anchors expressly encompassed (1) a call to recognize and accept the inevitable political nature of U.S. legal scholarship; (2) a concomitant call toward anti-subordination praxis to connect theory to action; (3) a commitment to build both intra-Latinx communities and inter-group coalitions; (4) a commitment to find commonalities while respecting difference; (5) a recognition of past critical outsider scholarship in new applications; (6) a commitment to ongoing self-critique, individually and collectively; and (7) a recognition of specificity and diversity in constructing LatCrit theory, praxis, and community. These early guiding commitments were rooted in substantive values, and accompanied by working postulates, that we likewise made explicit to help anchor our programmatic initiatives, and our mutual aspirations, over time and its exigencies

Afterword: What\u27s Next? Into a Third Decade of Latcrit Theory, Community, and Praxis

In this multi-vocal Afterword, we reflect-personally and collectively to help chart renewed agendas toward and through a third decade of LatCrit theory, community, and praxis. This personal collective exercise illustrates and reconsiders the functions, guideposts, values, and postulates for our shared programmatic work a framework for our daily work as individuals and teams through our portfolio of projects, which in turn emerged as a reflection and projection of LatCrit theory, community and praxis. These early anchors expressly encompassed (1) a call to recognize and accept the inevitable political nature of U.S. legal scholarship; (2) a concomitant call toward anti-subordination praxis to connect theory to action; (3) a commitment to build both intra-Latinx communities and inter-group coalitions; (4) a commitment to find commonalities while respecting difference; (5) a recognition of past critical outsider scholarship in new applications; (6) a commitment to ongoing self-critique, individually and collectively; and (7) a recognition of specificity and diversity in constructing LatCrit theory, praxis, and community. These early guiding commitments were rooted in substantive values, and accompanied by working postulates, that we likewise made explicit to help anchor our programmatic initiatives, and our mutual aspirations, over time and its exigencies

Afterword: What\u27s Next? Into a Third Decade of Latcrit Theory, Community, and Praxis

In this multi-vocal Afterword, we reflect-personally and collectively to help chart renewed agendas toward and through a third decade of LatCrit theory, community, and praxis. This personal collective exercise illustrates and reconsiders the functions, guideposts, values, and postulates for our shared programmatic work a framework for our daily work as individuals and teams through our portfolio of projects, which in turn emerged as a reflection and projection of LatCrit theory, community and praxis. These early anchors expressly encompassed (1) a call to recognize and accept the inevitable political nature of U.S. legal scholarship; (2) a concomitant call toward anti-subordination praxis to connect theory to action; (3) a commitment to build both intra-Latinx communities and inter-group coalitions; (4) a commitment to find commonalities while respecting difference; (5) a recognition of past critical outsider scholarship in new applications; (6) a commitment to ongoing self-critique, individually and collectively; and (7) a recognition of specificity and diversity in constructing LatCrit theory, praxis, and community. These early guiding commitments were rooted in substantive values, and accompanied by working postulates, that we likewise made explicit to help anchor our programmatic initiatives, and our mutual aspirations, over time and its exigencies

Parallel symbolic state-space exploration is difficult, but what is the alternative?

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

UV spectrophotometry method for the monitoring of galacto-oligosaccharides production

Monitoring the industrial production of galacto-oligosaccharides (GOS) requires a fast and accurate methodology able to quantify, in real time, the substrate level and the product yield. In this work, a simple, fast and inexpensive UV spectrophotometric method, together with partial least squares regression (PLS) and artificial neural networks (ANN), was applied to simultaneously estimate the products (GOS) and the substrate (lactose) concentrations in fermentation samples. The selected multiple models were trained and their prediction abilities evaluated by cross-validation and external validation being the results obtained compared with HPLC measurements. ANN models, generated from absorbance spectra data of the fermentation samples, gave, in general, the best performance being able to accurately and precisely predict lactose and total GOS levels, with standard error of prediction lower than 13 g kg 1 and coefficient of determination for the external validation set of 0.93–0.94, showing residual predictive deviations higher than five, whereas lower precision was obtained with the multiple model generated with PLS. The results obtained show that UV spectrophotometry allowed an accurate and non-destructive determination of sugars in fermentation samples and could be used as a fast alternative method for monitoring GOS production.Fundação para a Ciência e a Tecnologia (FCT) - Bolsa de doutouramento SFRH/BDE/15510/2004Agência da Inovação – Programa IDEIA (Potugal

Isokinetic eccentric exercise substantially improves mobility, muscle strength and size, but not postural sway metrics in older adults, with limited regression observed following a detraining period

© 2020, The Author(s). Introduction: Eccentric exercise can reverse age-related decreases in muscle strength and mass; however, no data exist describing its effects on postural sway. As the ankle may be more important for postural sway than hip and knee joints, and with older adults prone to periods of inactivity, the effects of two 6-week seated isokinetic eccentric exercise programmes, and an 8-week detraining period, were examined in 27 older adults (67.1 ± 6.0 years). Methods: Neuromuscular parameters were measured before and after training and detraining periods with subjects assigned to ECC (twice-weekly eccentric-only hip and knee extensor contractions) or ECCPF (identical training with additional eccentric-only plantarflexor contractions) training programmes. Results: Significant (P \u3c 0.05) increases in mobility (decreased timed-up-and-go time [− 7.7 to − 12.0%]), eccentric strength (39.4–58.8%) and vastus lateralis thickness (9.8–9.9%) occurred after both training programmes, with low-to-moderate weekly rate of perceived exertion (3.3–4.5/10) reported. No significant change in any postural sway metric occurred after either training programme. After 8 weeks of detraining, mobility (− 8.2 to − 11.3%), eccentric strength (30.5–50.4%) and vastus lateralis thickness (6.1–7.1%) remained significantly greater than baseline in both groups. Conclusion: Despite improvements in functional mobility, muscle strength and size, lower-limb eccentric training targeting hip, knee and ankle extensor muscle groups was not sufficient to influence static balance. Nonetheless, as the beneficial functional and structural adaptations were largely maintained through an 8-week detraining period, these findings have important implications for clinical exercise prescription as the exercise modality, low perceived training intensity, and adaptive profile are well suited to the needs of older adults