Allocating Security Expenditures under Knightian Uncertainty: an Info-Gap Approach

We apply the information gap approach to resource allocation under Knightian (non-probabilistic) uncertainty in order to study how best to allocate public resources betweencompeting defense measures. We demonstrate that when determining the level and composi-tion of defense spending in an environment of extreme uncertaintyvis-a-visthe likelihood ofarmed conflict and its outcomes, robust-satisficing expected utility will usually be preferableto expected utility maximisation. Moreover, our analysis suggests that in environments withunreliable information about threats to national security and their consequences, a desirefor robustness to model misspecification in the decision making process will imply greaterexpenditure on certain types of defense measures at the expense of others. Our results alsoprovide a positivist explanation of how governments seem to allocate security expendituresin practice

Allocating Security Expenditures under Knightian Uncertainty: an Info-Gap Approach

We apply the information gap approach to resource allocation under Knightian (non-probabilistic) uncertainty in order to study how best to allocate public resources between competing defense measures. We demonstrate that when determining the level and composition of defense spending in an environment of extreme uncertainty vis-a-vis the likelihood of armed conflict and its outcomes, robust-satisficing expected utility will usually be preferable to expected utility maximization. Moreover, our analysis suggests that in environments with unreliable information about threats to national security and their consequences, a desire for robustness to model misspecification in the decision making process will imply greater expenditure on certain types of defense measures at the expense of others. Our results also provide a positivist explanation of how governments seem to allocate security expenditures in practice

Allocating Security Expenditures under Knightian Uncertainty: an Info-Gap Approach

We apply the information gap approach to resource allocation under Knightian (non-probabilistic) uncertainty in order to study how best to allocate public resources between competing defense measures. We demonstrate that when determining the level and composition of defense spending in an environment of extreme uncertainty vis-a-vis the likelihood of armed conflict and its outcomes, robust-satisficing expected utility will usually be preferable to expected utility maximization. Moreover, our analysis suggests that in environments with unreliable information about threats to national security and their consequences, a desire for robustness to model misspecification in the decision making process will imply greater expenditure on certain types of defense measures at the expense of others. Our results also provide a positivist explanation of how governments seem to allocate security expenditures in practice

On the accuracy of solving confluent Prony systems

In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as frequency estimation and nonlinear Fourier inversion. Consequently, the question of stability of solution with respect to errors in the right-hand side becomes critical for the success of any particular application. We investigate the question of "maximal possible accuracy" of solving Prony-type systems, putting stress on the "local" behavior which approximates situations with low absolute measurement error. The accuracy estimates are formulated in very simple geometric terms, shedding some light on the structure of the problem. Numerical tests suggest that "global" solution techniques such as Prony's algorithm and ESPRIT method are suboptimal when compared to this theoretical "best local" behavior

Evolution of constrained layer damping using a cellular automaton algorithm

Constrained layer damping (CLD) is a highly effective passive vibration control strategy if optimized adequately. Factors controlling CLD performance are well documented for the flexural modes of beams but not for more complicated mode shapes or structures. The current paper introduces an approach that is suitable for locating CLD on any type of structure. It follows the cellular automaton (CA) principle and relies on the use of finite element models to describe the vibration properties of the structure. The ability of the algorithm to reach the best solution is demonstrated by applying it to the bending and torsion modes of a plate. Configurations that give the most weight-efficient coverage for each type of mode are first obtained by adapting the existing 'optimum length' principle used for treated beams. Next, a CA algorithm is developed, which grows CLD patches one at a time on the surface of the plate according to a simple set of rules. The effectiveness of the algorithm is then assessed by comparing the generated configurations with the known optimum ones

Prediction of immediate ventricular arrhythmias after coronary artery ligation

AbstractObjectives. Our aim was to test the hypothesis that increased beat to beat morphologic variations in the body surface electrocardiogram (ECG) are associated with fragmented diastolic electrical activity that appears after coronary artery ligation and to correlate the appearance of spontaneous ventricular fibrillation after coronary ligation with the magnitude of the ECG beat to beat variability.Background. Unstable and variably delayed electrical activation precedes the development of ventricular fibrillation in dogs with acute ischemia. Detection of these highly variable low amplitude signals from the body surface is currently impossible. We have developed a system designed to measure the degree of beat to beat variability of the ECG.Methods. With high fidelity electrocardiography, subtle beat to beat ECG morphologic variations were detected in epicardial and body surface electrograms and quantified as the variance of the ECG voltage at specific points of the cardiac cycle. The ratio of the variance at the QRS offset to that of the QRS onset (beat to beat variability index) was then calculated.Results. Ventricular fibrillation developed in 12 of 27 dogs after left anterior descending coronary artery ligation. In 7 of the 12 dogs it occurred immediately (<15 min) after ligation; in the other 5 it developed late (15 min) after ligation. Dogs with subsequently immediate ventricular fibrillation had a significantly higher beat to beat variability index than that of dogs with late or no ventricular fibrillation both before coronary ligation (4.7 ± 1.4 vs. 1.1 ± 0.2 and 0.8 ± 0.1, respectively, p < 0.001) and after ligation (6.4 ± 2.6, 1.0 ± 0.6 and 1.2 ± 0.6, respectively, p < 0.001). In dogs that developed ventricular fibrillation immediately after coronary ligation, the arrhythmia was preceded by fragmented diastolic electrical activity on the epicardial electrogram and a simultaneous increase in the beat to beat morphologic variability of the terminal portion of the body surface ECG QRS complex.Conclusions. Beat to beat QRS offset morphologic variations appear to be increased before and further increased after coronary artery ligation in dogs that develop ventricular fibrillation immediately after ligation. Increased beat to beat variability index may be associated with the presence of electrophysiologic instability and can predict early ventricular fibrillation

ProNodal acts via FGFR3 to govern duration of Shh expression in the prechordal mesoderm

The secreted glycoprotein sonic hedgehog (Shh) is expressed in the prechordal mesoderm, where it plays a crucial role in induction and patterning of the ventral forebrain. Currently little is known about how Shh is regulated in prechordal tissue. Here we show that in the embryonic chick, Shh is expressed transiently in prechordal mesoderm, and is governed by unprocessed Nodal. Exposure of prechordal mesoderm microcultures to Nodal-conditioned medium, the Nodal inhibitor CerS, or to an ALK4/5/7 inhibitor reveals that Nodal is required to maintain both Shh and Gsc expression, but whereas Gsc is largely maintained through canonical signalling, Nodal signals through a non-canonical route to maintain Shh. Further, Shh expression can be maintained by a recombinant Nodal cleavage mutant, proNodal, but not by purified mature Nodal. A number of lines of evidence suggest that proNodal acts via FGFR3. ProNodal and FGFR3 co-immunoprecipitate and proNodal increases FGFR3 tyrosine phosphorylation. In microcultures, soluble FGFR3 abolishes Shh without affecting Gsc expression. Further, prechordal mesoderm cells in which Fgfr3 expression is reduced by Fgfr3 siRNA fail to bind to proNodal. Finally, targeted electroporation of Fgfr3 siRNA to prechordal mesoderm in vivo results in premature Shh downregulation without affecting Gsc. We report an inverse correlation between proNodal-FGFR3 signalling and pSmad1/5/8, and show that proNodal-FGFR3 signalling antagonises BMP-mediated pSmad1/5/8 signalling, which is poised to downregulate Shh. Our studies suggest that proNodal/FGFR3 signalling governs Shh duration by repressing canonical BMP signalling, and that local BMPs rapidly silence Shh once endogenous Nodal-FGFR3 signalling is downregulated

An improved lower bound for (1,<=2)-identifying codes in the king grid

We call a subset $C$ of vertices of a graph $G$ a $(1,\leq \ell)$-identifying code if for all subsets $X$ of vertices with size at most $\ell$, the sets $\{c\in C |\exists u \in X, d(u,c)\leq 1\}$ are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a $(1,\leq 2)$-identifying code in the king grid with density 3/7 and that there are no such identifying codes with density smaller than 5/12. Using a suitable frame and a discharging procedure, we improve the lower bound by showing that any $(1,\leq 2)$-identifying code of the king grid has density at least 47/111