Closed classes of functions, generalized constraints and clusters

Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois theory of functions and generalized constraints is extended to infinite domains. Furthermore, classes of operations on arbitrary non-empty domains that are closed under permutation of variables, addition of dummy variables and composition are characterized in terms of clusters, and a Galois connection is established between operations and clusters.Comment: 21 page

The Governmental-Proprietary Distinction in Constitutional Law

The governmental-proprietary distinction has led a stormy life. Courts have characterized it as “illusory,” a “quagmire,” a “rule of law that is inherently unsound,” and as a “talismanic formula” that results in “unenlightening characterizations of States’ activities.” Commentators have branded the distinction as “probably one of the most unsatisfactory known to the law,” have questioned its internal coherence, and have dismissed it as irrelevant in constitutional decisions. The distinction, however, clings stubbornly to life, appearing in a remarkably wide range of cases. The United States Supreme Court itself appears ambivalent about its worth. In some cases, the Court has rejected the distinction and has directed scathing criticism toward it, but the Court also has found the distinction useful for a variety of purposes. In recent years, the distinction has appeared in Supreme Court opinions concerning the sovereign immunity of foreign nations for their acts of state, “the application of the antitrust laws to state and local governments,” the negative implications of the commerce clause’s (and perhaps the affirmative powers of Congress under that clause), the scope of state immunity from suit under the eleventh amendment, and the constitutional rights of individuals against the state. The distinction\u27s persistence in the face of unrelenting criticism raises the question whether it may be a more subtle and intelligible doctrine than its reputation would suggest. This article pursues that question with respect to the uses to which the Court has put the distinction in constitutional cases. In view of the confusion surrounding the distinction, it is useful to begin the inquiry by mapping the ground that will be covered

Equational characterization of Boolean function classes

Cataloged from PDF version of article.Several noteworthy classes of Boolean functions can be characterized by algebraic identities (e.g. the class of positive functions consists of all functions f satisfying the identity f(x) V f(y) V f(x V y) = f(x V y)). We give algebraic identities for several of the most frequently analyzed classes of Boolean functions (including Horn, quadratic, supermodular, and submodular functions) and proceed then to the general question of which classes of Boolean functions can be characterized by algebraic identities. We answer this question for function classes closed under addition of inessential (irrelevant) variables. Nearly all classes of interest have this property. We show that a class with this property has a characterization by algebraic identities if and only if the class is closed under the operation of variable identification. Moreover, a single identity suffices to characterize a class if and only if the number of minimal forbidden identification minors is finite. Finally, we consider characterizations by general first-order sentences, rather than just identities. We show that a class of Boolean functions can be described by an appropriate set of such first-order sentences if and only if it is closed under permutation of variables. © 2000 Elsevier Science B.V. All rights reserved

Dynamic Adaptation of Rules for Temporal Event Correlation in Distributed Systems

Event correlation is essential to realizing self-managing distributed systems. For example, distributed systems often require that events be correlated from multiple systems using temporal patterns to detect denial of service attacks and to warn of problems with business critical applications that run on multiple servers. This paper addresses how to specify timer values for temporal patterns so as to manage the trade-off between false alarms and undetected alarms. A central concern is addressing the variability of event propagation delays due to factors such as contention for network and server resources. To this end, we develop an architecture and an adaptive control algorithm that dynamically compensate for variations in propagation delays. Our approach makes Management Stations more autonomic by avoiding the need for manual adjustments of timer values in temporal rules. Further, studies we conducted of a testbed system suggest that our approach produces results that are at least as good as an optimal fixed setting of timer values

Proof of a conjecture of Polya on the zeros of successive derivatives of real entire functions

We prove Polya's conjecture of 1943: For a real entire function of order greater than 2, with finitely many non-real zeros, the number of non-real zeros of the n-th derivative tends to infinity with n. We use the saddle point method and potential theory, combined with the theory of analytic functions with positive imaginary part in the upper half-plane.Comment: 26 page

An ANGPTL4-ceramide-protein kinase Cζ axis mediates chronic glucocorticoid exposure-induced hepatic steatosis and hypertriglyceridemia in mice.

Chronic or excess glucocorticoid exposure causes lipid disorders such as hypertriglyceridemia and hepatic steatosis. Angptl4 (angiopoietin-like 4), a primary target gene of the glucocorticoid receptor in hepatocytes and adipocytes, is required for hypertriglyceridemia and hepatic steatosis induced by the synthetic glucocorticoid dexamethasone. Angptl4 has also been shown to be required for dexamethasone-induced hepatic ceramide production. Here, we further examined the role of ceramide-mediated signaling in hepatic dyslipidemia caused by chronic glucocorticoid exposure. Using a stable isotope-labeling technique, we found that dexamethasone treatment induced the rate of hepatic de novo lipogenesis and triglyceride synthesis. These dexamethasone responses were compromised in Angptl4-null mice (Angptl4-/-). Treating mice with myriocin, an inhibitor of the rate-controlling enzyme of de novo ceramide synthesis, serine palmitoyltransferase long-chain base subunit 1 (SPTLC1)/SPTLC2, decreased dexamethasone-induced plasma and liver triglyceride levels in WT but not Angptl4-/- mice. We noted similar results in mice infected with adeno-associated virus-expressing small hairpin RNAs targeting Sptlc2. Protein phosphatase 2 phosphatase activator (PP2A) and protein kinase Cζ (PKCζ) are two known downstream effectors of ceramides. We found here that mice treated with an inhibitor of PKCζ, 2-acetyl-1,3-cyclopentanedione (ACPD), had lower levels of dexamethasone-induced triglyceride accumulation in plasma and liver. However, small hairpin RNA-mediated targeting of the catalytic PP2A subunit (Ppp2ca) had no effect on dexamethasone responses on plasma and liver triglyceride levels. Overall, our results indicate that chronic dexamethasone treatment induces an ANGPTL4-ceramide-PKCζ axis that activates hepatic de novo lipogenesis and triglyceride synthesis, resulting in lipid disorders