Existing or planned power grids need to evaluate survivability under extreme events, like a number of peak load overloading conditions, which could possibly cause system collapses (i.e. blackouts). For realistic extreme events that are correlated or share similar patterns, it is reasonable to expect that the dominant vulnerability or failure sources behind them share the same locations but with different severity. Early warning diagnosis that proactively identifies the key vulnerabilities responsible for a number of system collapses of interest can significantly enhance resilience. This paper proposes a multi-period sparse optimization method, enabling the discovery of persistent failure sources across a sequence of collapsed systems with increasing system stress, such as rising demand or worsening contingencies. This work defines persistency and efficiently integrates persistency constraints to capture the “hidden” evolving vulnerabilities. Circuit-theory based power flow formulations and circuit-inspired optimization heuristics are used to facilitate the scalability of the method. Experiments on benchmark systems show that the method reliably tracks persistent vulnerability locations under increasing load stress, and solves with scalability to large systems (on average taking around 200 s per scenario on 2000+ bus systems).
In an earlier paper, we proved that Montgomery's Pair Correlation Conjecture (PCC) for zeros of the Riemann zeta-function can be used to prove without the assumption of the Riemann Hypothesis (RH) that asymptotically 100% of the zeros are both simple and on the critical line. This is based on a method of Gallagher and Mueller from 1978. We formulate an appropriate form of the Alternative Hypothesis (AH), which determines a different PCC, and, using the same method as above, prove that asymptotically, 100% of the zeros are both simple and on the critical line. As in our previous paper, we do not assume RH.
As financial incentives for EVs wane and price parity approaches, engaging mainstream adopters is critical to sustaining market growth. While early adopters are driven by environmentalism and proactive information-seeking, the broader market remains hesitant due to knowledge gaps regarding EV benefits. We evaluate how communication of state-specific emission estimates for five vehicle types (ICE, HEV, PHEV, BEV, and FCEV) influences vehicle perceptions, rankings, and fleet composition. Surveying 908 participants across four states (CA, FL, PA, TX), we find that, while emissions information shifts vehicle rankings, political identity and charging feasibility remain the primary determinants of top preferences. Furthermore, participants favor fleets with a diverse composition over a single technology. Our findings suggest that providing state-level emission estimates effectively reshapes consumer preferences and reduces the desired share of high-emission vehicles. This research provides a strategic framework for policymakers and manufacturers to sustain market momentum through transparency and targeted communication.
Introduction: Significant effort has been put towards mapping patterns of atrophy in the cerebral cortex that are related to pathological aging, including the characteristic patterns of neurodegeneration in Alzheimer's disease (AD). In contrast, brain structural patterns that support preserved or even exceptional cognition throughout the adult age-span and especially in later life are much less known. It is possible that superior cognitive performance in late life is supported by a preservation of brain structures vulnerable to typical aging. Alternatively, elevated performance could be related to preservation of brain regions vulnerable to age-associated pathology. Examination of individuals that exhibit superior cognition throughout the adult lifespan may provide unique insights into neural mechanisms that support cognitive resilience in late life. Methods: We examined cross-sectional associations between cortical brain structure and cognitive performance across three stages of adulthood: midlife (36-59), young-old (60-79), and older adults (80+) in typically aging individuals enrolled as part of the Human Connectome Project Lifespan-Aging (HCP-A)/Aging Adult Brain Connectome (AABC) studies. Participants were considered generally healthy and excluded for significant and/or atypical health conditions for their demographic category, including a clinical diagnosis of cognitive impairment or dementia. Domain-specific cognitive factor scores representing memory, fluid intelligence, and crystalized intelligence were sex-stratified and residualized relative to age, and participants were classified as high, middle, or low performers based on their unique performance relative to the study sample. Results: In the full sample, high performers demonstrated greater cortical thickness in regions of somatomotor, visual, and auditory cortices, as well as cortical areas in the frontal, parietal, and insular cortices (e.g., 5m, LIPv, MBelt). We also found associations between medial temporal and cingulate cortical thickness and cognitive performance, but only for select analyses. Group differences in cortical thickness were greatest when contrasting high and low performers for fluid intelligence compared to the other cognitive factors and were most prominent in the midlife participants compared to the other age strata. These group differences were primarily driven by reduced cortical thickness in the low performing individuals in the younger age bins relative to the 'typically' performing sample. Effects were rather limited when contrasting high and low performers in the 80+ age group. The cortical areas of high statistical significance appeared to show a cross-sectional convergence effect, such that the differences in cortical thickness between high vs. low cognitive performance groups diminished with increasing age. Despite lower statistical power, effect sizes were greatest when contrasting individuals at the extremes of performance (e.g., top 10% vs. bottom 10% performers). These effects were robust to subsample replications using longitudinally defined cognitive classifications. Discussion: Elevated cognitive performance was cross-sectionally associated with increased regional cortical thickness and effects were most prominent in mid-life compared to later ages. Notably, contrary to brain regions that may be expected to support such high-order cognitive performance, a significant portion of primary sensory, motor, and insular cortical areas exhibited group differences between the high- and low-performing groups in this relatively younger age group. Group differences were due to lower thickness in these regions in the low performing group relative to the typical performers. In contrast to the younger portion of the sample, regions typically considered vulnerable to Alzheimer's disease (i.e., regions in the medial temporal lobe) were only infrequently implicated. These results suggest that specific patterns of cortical brain structural integrity including preserved thickness of primary motor and sensory cortical regions may be a necessary but not sufficient mechanism supporting superior cognitive abilities in earlier adulthood, while alternate neural mechanisms may support cognitive resilience later in life. These results must be interpreted with caution given the cross-sectional nature of this study. Cognitive capacity can only be estimated from a single timepoint, and several factors contribute to inter-individual variation that will not be accounted for in the models applied here. Longitudinal assessment of cognitive resilience in the HCP-A/AABC cohort will be performed in future work. ### Competing Interest Statement DHS has a financial interest in Niji Corp. National Institute of Aging of the National Institutes of Health, U19AG073585, U01AG052564 McDonnell Center for Neuroscience at Washington University in St. Louis
We give a geometric model for the non-τ-rigid modules over acyclic path algebras of type D˜n. Similar models have been provided for module categories over path algebras of types An,Dn, and A˜n as well as the τ-rigid modules of type D˜n. A major draw of these geometric models is the “intersection-dimension formulas” they often come with. These formulas give an equality between the intersection number of the curves representing the modules in the geometric model and the dimension of the extension spaces between the two modules. This formula allows us to calculate the homological data between two modules combinatorially. Since there are infinitely many distinct homogeneous stable tubes in the regular component of the Auslander-Reiten quiver of type D˜n, all of which are disjoint, our geometric data requires an extra decoration on the admissible edges in our geometric model to prevent intersections between curves corresponding to modules in distinct stable tubes of the Auslander-Reiten quiver.
