Average-case complexity of detecting cliques

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 79-83).The computational problem of testing whether a graph contains a complete subgraph of size k is among the most fundamental problems studied in theoretical computer science. This thesis is concerned with proving lower bounds for k-CLIQUE, as this problem is known. Our results show that, in certain models of computation, solving k-CLIQUE in the average case requires Q(nk/4) resources (moreover, k/4 is tight). Here the models of computation are bounded-depth Boolean circuits and unbounded-depth monotone circuits, the complexity measure is the number of gates, and the input distributions are random graphs with an appropriate density of edges. Such random graphs (the well-studied Erdos-Renyi random graphs) are widely believed to be a source of computationally hard instances for clique problems (as Karp suggested in 1976). Our results are the first unconditional lower bounds supporting this hypothesis. For bounded-depth Boolean circuits, our average-case hardness result significantly improves the previous worst-case lower bounds of Q(nk/Poly(d)) for depth-d circuits. In particular, our lower bound of Q(nk/ 4 ) has no noticeable dependence on d for circuits of depth d ; k- log n/log log n, thus bypassing the previous "size-depth tradeoffs". As a consequence, we obtain a novel Size Hierarchy Theorem for uniform AC0 . A related application answers a longstanding open question in finite model theory (raised by Immerman in 1982): we show that the hierarchy of bounded-variable fragments of first-order logic is strict on finite ordered graphs. Additional results of this thesis characterize the average-case descriptive complexity of k-CLIQUE through the lens of first-order logic.by Benjamin Rossman.Ph.D

An O(n^3)-Time Algorithm for Tree Edit Distance

The {\em edit distance} between two ordered trees with vertex labels is the minimum cost of transforming one tree into the other by a sequence of elementary operations consisting of deleting and relabeling existing nodes, as well as inserting new nodes. In this paper, we present a worst-case $O(n^3)$-time algorithm for this problem, improving the previous best $O(n^3\log n)$-time algorithm~\cite{Klein}. Our result requires a novel adaptive strategy for deciding how a dynamic program divides into subproblems (which is interesting in its own right), together with a deeper understanding of the previous algorithms for the problem. We also prove the optimality of our algorithm among the family of \emph{decomposition strategy} algorithms--which also includes the previous fastest algorithms--by tightening the known lower bound of $\Omega(n^2\log^2 n)$~\cite{Touzet} to $\Omega(n^3)$, matching our algorithm's running time. Furthermore, we obtain matching upper and lower bounds of $\Theta(n m^2 (1 + \log \frac{n}{m}))$ when the two trees have different sizes $m$ and~$n$, where $m < n$.Comment: 10 pages, 5 figures, 5 .tex files where TED.tex is the main on

Stress-related emotional and behavioural impact following the first COVID-19 outbreak peak

The COVID-19 pandemic poses multiple psychologically stressful challenges and is associated with an increased risk for mental illness. Previous studies have focused on the psychopathological symptoms associated with the outbreak peak. Here, we examined the behavioural and mental-health impact of the pandemic in Israel using an online survey, during the six weeks encompassing the end of the first outbreak and the beginning of the second. We used clinically validated instruments to assess anxiety- and depression-related emotional distress, symptoms, and coping strategies, as well as questions designed to specifically assess COVID-19-related concerns. Higher emotional burden was associated with being female, younger, unemployed, living in high socioeconomic status localities, having prior medical conditions, encountering more people, and experiencing physiological symptoms. Our findings highlight the environmental context and its importance in understanding individual ability to cope with the long-term stressful challenges of the pandemic

Passive Leg Movement and Nitric Oxide-Mediated Vascular Function: The Impact of Age

In young healthy men, passive leg movement (PLM) elicits a robust nitric oxide (NO)-dependent increase in leg blood flow (LBF), thus providing a novel approach to assess NO-mediated vascular function. While the magnitude of the LBF response to PLM is markedly reduced with age, the role of NO in this attenuated response in the elderly is unknown. Therefore, this study sought to determine the contribution of NO in the PLM-induced LBF with age. Fourteen male subjects (7 young, 24 ± 1 yr; and 7 old, 75 ± 3 yr) underwent PLM with and without NO synthase (NOS) inhibition achieved by intra-arterial infusion of N(G)-monomethyl-L-arginine (L-NMMA). LBF was determined second-by-second by Doppler ultrasound, and central hemodynamics were measured by finger photoplethysmography. NOS inhibition blunted the PLM-induced peak increase in LBF in the young (control: 668 ± 106; L-NMMA: 431 ± 95 Δml/min; P = 0.03) but had no effect in the old (control: 266 ± 98; L-NMMA: 251 ± 92 Δml/min; P = 0.59). Likewise, the magnitude of the reduction in the overall (i.e., area under the curve) PLM-induced LBF response to NOS inhibition was less in the old (LBF: -31 ± 18 ml) than the young (LBF: -129 ± 21 ml; P \u3c 0.01). These findings suggest that the age-associated reduction in PLM-induced LBF in the elderly is primarily due to a reduced contribution to vasodilation from NO and therefore support the use of PLM as a novel approach to assess NO-mediated vascular function across the lifespan

Endothelin-A-Mediated Vasoconstriction during Exercise with Advancing Age

The endothelin-1 vasoconstrictor pathway contributes to age-related elevations in resting peripheral vascular tone primarily through activation of the endothelin subtype A (ET(A)) receptor. However, the regulatory influence of ET(A)-mediated vasoconstriction during exercise in the elderly is unknown. Thus, in 17 healthy volunteers (n = 8 young, 24±2 years; n = 9 old, 70±2 years), we examined leg blood flow, mean arterial pressure, leg arterial-venous oxygen (O2) difference, and leg O2 consumption (VO2) at rest and during knee-extensor exercise before and after intra-arterial administration of the ET(A) antagonist BQ-123. During exercise, BQ-123 administration increased leg blood flow to a greater degree in the old (+29±5 mL/min/W) compared with the young (+16±3 mL/min/W). The increase in leg blood flow with BQ-123 was accompanied by an increase in leg VO2 in both groups, suggesting a reduced efficiency following ET(A) receptor blockade. Together, these findings have identified an age-related increase in ET(A)-mediated vasoconstrictor activity that persists during exercise, suggesting an important role of this pathway in the regulation of exercising skeletal muscle blood flow and maintenance of arterial blood pressure in the elderly

Taming the Sleeping Giant : The Role of Endothelin-1 in the Regulation of Skeletal Muscle Blood Flow and Arterial Blood Pressure during Exercise

The cardiovascular response to exercise is governed by a combination of vasodilating and vasoconstricting influences that optimize exercising muscle perfusion while protecting mean arterial pressure (MAP). The degree to which endogenous endothelin (ET)-1, the body\u27s most potent vasoconstrictor, participates in this response is unknown. Thus, in eight young (24 ± 2 yr), healthy volunteers, we examined leg blood flow, MAP, tissue oxygenation, heart rate, leg arterial-venous O2 difference, leg O2 consumption, pH, and net ET-1 and lactate release at rest and during knee extensor exercise (0, 5, 10, 15, 20, and 30 W) before and after an intra-arterial infusion of BQ-123 [ET subtype A (ETA) receptor antagonist]. At rest, BQ-123 did not evoke a change in leg blood flow or MAP. During exercise, net ET-1 release across the exercising leg increased approximately threefold. BQ-123 increased leg blood flow by ∼20% across all work rates (changes of 113 ± 76, 176 ± 83, 304 ± 108, 364 ± 130, 502 ± 117, and 570 ± 178 ml/min at 0, 5, 10, 15, 20, and 30 W, respectively) and attenuated the exercise-induced increase in MAP by ∼6%. The increase in leg blood flow was accompanied by a ∼9% increase in leg O2 consumption with an unchanged arterial-venous O2 difference and deoxyhemoglobin, suggesting a decline in intramuscular efficiency after ETA receptor blockade. Together, these findings identify a significant role of the ET-1 pathway in the cardiovascular response to exercise, implicating vasoconstriction via the ETA receptor as an important mechanism for both the restraint of blood flow in the exercising limb and maintenance of MAP in healthy, young adults

Endogenous Endothelin-1 and Femoral Artery Shear Rate: Impact of Age and Implications for Atherosclerosis

Background: Both altered shear rate and endothelin-1 (ET-1) are associated with the age-related development of atherosclerosis. However, the role of ET-1, a potent endogenous vasoconstrictor, in altering shear rate in humans, especially in the atherosclerotic-prone vasculature of the leg, is unknown. Therefore, this study examined the contribution of ET-1 to the age-related alterations in common femoral artery (CFA) shear rate. Method: BQ-123, a specific endothelin type A (ETA) receptor antagonist, was infused into the CFA, and diameter and blood velocity were measured by Doppler ultrasound in young (n = 8, 24 ± 2 years) and old (n = 9, 70 ± 2 years) study participants. Results and conclusion: The old had greater intima–media thickening in the CFA, indicative of a preatherogenic phenotype. Prior to infusion, the old study participants exhibited reduced mean shear rate (27 ± 3/s) compared with the young study participants (62 ± 9/s). This difference was likely driven by attenuated antegrade shear rate in the old as retrograde shear rate was similar in the young and old. Inhibition of ETA receptors, by BQ-123, increased leg blood flow in the old, but not in the young, abolishing age-related differences. Older study participants had a larger CFA (young: 0.82 ± 0.03 cm, old: 0.99 ± 0.03 cm) in which BQ-123 induced significant vasodilation (5.1 ± 1.0%), but had no such effect in the young (−0.8 ± 0.8%). Interestingly, despite the age-specific, BQ-123-induced increase in leg blood flow and CFA diameter, shear rate patterns remained largely unchanged. Therefore, ET-1, acting through the ETA receptors, exerts a powerful age-specific vasoconstriction. However, removal of this vasoconstrictor stimulus does not augment mean shear rate in the old