The Creative Life of Law: Improvisation, Between Tradition and Suspicion

Originally applying solely to chefs, waiters, dishwashers and the like, New York City (NYC) regulations governing cabaret employees were altered in 1943 to include musicians and entertainers, who until the late 1960’s would be required to hold a NYC Cabaret Employee’s Identification Card. The introduction of these notorious “police cards” occurred roughly contemporaneously to the emergence in after-hours night clubs in Harlem of a new and supposedly “wild”, improvisatory brand of jazz: bebop. This article adds to the many rather practical theories on why these cards were introduced a more abstract discussion coined in terms of the relationship between suspicion and tradition and focusing on differing essences of law and improvisatory jazz. While law breathes tradition and is suspicious of improvisation and unpredictability, the converse is true of jazz. Allusion to tradition in jazz improvisation is often viewed as a betrayal of its creative and spontaneous nature. And yet it is only through its departure from the stable transmission of past meaning that improvisation gains meaning. Law, in contrast, while appearing to be entirely composed of tradition, to transmit some sort of determinate and fixed meaning, is constantly betraying itself. As no two legal actions can be exactly the same, judges must improvise on tradition and past precedent every time they are asked to decide a case. Law can thus neither dispense with nor be completely determined by tradition. The legal decision instead lies on the border between what it “is” and what it otherwise could be and every judicial act is, in some sense, a species of improvisation. This article uses the cabaret cards to explore this uncertain terrain between law and improvisation, between tradition and suspicion.

Partial Cooperative Equilibria: Existence and Characterization

We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful.

Robust Dynamic Pricing Over Infinite Horizon in The Presence of Model Uncertainty( 2* Journal)

This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

SK1 of graded division algebras

The reduced Whitehead group $\SK$ of a graded division algebra graded by a torsion-free abelian group is studied. It is observed that the computations here are much more straightforward than in the non-graded setting. Bridges to the ungraded case are then established by the following two theorems: It is proved that $\SK$ of a tame valued division algebra over a henselian field coincides with $\SK$ of its associated graded division algebra. Furthermore, it is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its quotient division algebra. The first theorem gives the established formulas for the reduced Whitehead group of certain valued division algebras in a unified manner, whereas the latter theorem covers the stability of reduced Whitehead groups, and also describes $\SK$ for generic abelian crossed products.

Blood pressure lowering in patients without prior cerebrovascular disease for prevention of cognitive impairment and dementia

Background: This is an update of a previous review (McGuinness 2006). Hypertension and cognitive impairment are prevalent in older people. Hypertension is a direct risk factor for vascular dementia (VaD) and recent studies have suggested hypertension impacts upon prevalence of Alzheimer's disease (AD). Therefore does treatment of hypertension prevent cognitive decline?
Objectives: To assess the effects of blood pressure lowering treatments for the prevention of dementia and cognitive decline in patients with hypertension but no history of cerebrovascular disease.
Search strategy: The Specialized Register of the Cochrane Dementia and Cognitive Improvement Group, The Cochrane Library, MEDLINE, EMBASE, PsycINFO, CINAHL, LILACS as well as many trials databases and grey literature sources were searched on 13 February 2008 using the terms: hypertens$ OR anti-hypertens$. Selection criteria: Randomized, double-blind, placebo controlled trials in which pharmacological or non-pharmacological interventions to lower blood pressure were given for at least six months.
Data collection and analysis: Two independent reviewers assessed trial quality and extracted data. The following outcomes were assessed: incidence of dementia, cognitive change from baseline, blood pressure level, incidence and severity of side effects and quality of life.
Main results: Four trials including 15,936 hypertensive subjects were identified. Average age was 75.4 years. Mean blood pressure at entry across the studies was 171/86 mmHg. The combined result of the four trials reporting incidence of dementia indicated no significant difference between treatment and placebo (236/7767 versus 259/7660, Odds Ratio (OR) = 0.89, 95% CI 0.74, 1.07) and there was considerable heterogeneity between the trials. The combined results from the three trials reporting change in Mini Mental State Examination (MMSE) did not indicate a benefit from treatment (Weighted Mean Difference (WMD) = 0.42, 95%CI 0.30, 0.53). Both systolic and diastolic blood pressure levels were reduced significantly in the three trials assessing this outcome (WMD = -10.22, 95% CI -10.78, -9.66 for systolic blood pressure, WMD = -4.28, 95% CI -4.58, -3.98 for diastolic blood pressure). Three trials reported adverse effects requiring discontinuation of treatment and the combined results indicated no significant difference (OR = 1.01, 95% CI 0.92, 1.11). When analysed separately, however, more patients on placebo in Syst Eur 1997 were likely to discontinue treatment due to side effects; the converse was true in SHEP 1991. Quality of life data could not be analysed in the four studies. Analysis of the included studies in this review was problematic as many of the control subjects received antihypertensive treatment because their blood pressures exceeded pre-set values. In most cases the study became a comparison between the study drug against a usual antihypertensive regimen.
Authors' conclusions: There is no convincing evidence fromthe trials identified that blood pressure lowering in late-life prevents the development of dementia or cognitive impairment in hypertensive patients with no apparent prior cerebrovascular disease. There were significant problems identified with analysing the data, however, due to the number of patients lost to follow-up and the number of placebo patients who received active treatment. This introduced bias. More robust results may be obtained by conducting a meta-analysis using individual patient data.

Reducing Uncertainty in Aeroelastic Flutter Boundaries Using Experimental Data

Flutter prediction as currently practiced is usually deterministic, with a single structural model used to represent an aircraft. By using interval analysis to take into account structural variability, recent work has demonstrated that small changes in the structure can lead to very large changes in the altitude at which
utter occurs (Marques, Badcock, et al., J. Aircraft, 2010). In this follow-up work we examine the same phenomenon using probabilistic collocation (PC), an uncertainty quantification technique which can eficiently propagate multivariate stochastic input through a simulation code,
in this case an eigenvalue-based fluid-structure stability code. The resulting analysis predicts the consequences of an uncertain structure on incidence of
utter in probabilistic terms { information that could be useful in planning
flight-tests and assessing the risk of structural failure. The uncertainty in
utter altitude is confirmed to be substantial. Assuming that the structural uncertainty represents a epistemic uncertainty regarding the
structure, it may be reduced with the availability of additional information { for example aeroelastic response data from a flight-test. Such data is used to update the structural uncertainty using Bayes' theorem. The consequent
utter uncertainty is significantly reduced across the entire Mach number range.

Optical source model for the 23.2-23.6 nm radiation from the multielement germanium soft X-ray laser

Distributions of source intensity in two dimensions (designated the source model), averaged over a single laser pulse, based on experimental measurements of spatial coherence, are considered for radiation from the unresolved 23.2/23.6 nm spectral lines from the germanium collisional X-ray laser. The model derives from measurements of the visibility of Young slit interference fringes determined by a method based on the Wiener-Khinchin theorem. Output from amplifiers comprising three and four target elements have similar coherence properties in directions within the horizontal plane corresponding to strong plasma refraction effects and fitting the coherence data shows source dimensions (FWHM) are similar to 26 mu m (horizontal), significantly smaller than expected by direct imaging, and similar to 125 mu m (vertical: equivalent to the height of the driver excitation). (C) 1999 Elsevier Science B.V. All rights reserved.

Coherence and bandwidth measurements of harmonics generated from solid surfaces irradiated by intense picosecond laser pulses

We present measurements of the transverse and longitudinal coherence lengths of the fourth harmonic of a 1053-nm, 2.5-ps laser generated during high-intensity (up to 10(19) W cm(-2)) interactions with a solid target. Coherence lengths were measured by use of a Young's double-slit interferometer. The effective source size, as defined by the Van Cittert-Zernicke theorem, was found to be 10-12 mu m, and the coherence time was observed to be in the range 0.02-0.4 ps.

A sequential algorithm for sparse support vector classifiers

Support vector machines (SVMs), though accurate, are not preferred in applications requiring high classification speed or when deployed in systems of limited computational resources, due to the large number of support vectors involved in the model. To overcome this problem we have devised a primal SVM method with the following properties: (1) it solves for the SVM representation without the need to invoke the representer theorem, (2) forward and backward selections are combined to approach the final globally optimal solution, and (3) a criterion is introduced for identification of support vectors leading to a much reduced support vector set. In addition to introducing this method the paper analyzes the complexity of the algorithm and presents test results on three public benchmark problems and a human activity recognition application. These applications demonstrate the effectiveness and efficiency of the proposed algorithm.


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Hardware elliptic curve cryptographic processor over GF(p)

A novel hardware architecture for elliptic curve cryptography (ECC) over GF(p) is introduced. This can perform the main prime field arithmetic functions needed in these cryptosystems including modular inversion and multiplication. This is based on a new unified modular inversion algorithm that offers considerable improvement over previous ECC techniques that use Fermat's Little Theorem for this operation. The processor described uses a full-word multiplier which requires much fewer clock cycles than previous methods, while still maintaining a competitive critical path delay. The benefits of the approach have been demonstrated by utilizing these techniques to create a field-programmable gate array (FPGA) design. This can perform a 256-bit prime field scalar point multiplication in 3.86 ms, the fastest FPGA time reported to date. The ECC architecture described can also perform four different types of modular inversion, making it suitable for use in many different ECC applications. © 2006 IEEE.

A multi-fibre multi-layer representative volume element (M2RVE) for prediction of matrix and interfacial damage in composite laminates

Multiscale micro-mechanics theory is extensively used for the prediction of the material response and damage analysis of unidirectional lamina using a representative volume element (RVE). Th is paper presents a RVE-based approach to characterize the materi al response of a multi-fibre cross-ply laminate considering the effect of matrix damage and fibre-matrix interfacial strength. The framework of the homogenization theory for periodic media has been used for the analysis of a 'multi-fibre multi-layer representative volume element' (M2 RVE) representing cross-ply laminate. The non-homogeneous stress-strain fields within the M2RVE are related to the average stresses and strains by using Gauss theorem and the Hill-Mandal strain energy equivalence principle. The interfacial bonding strength affects the in-plane shear stress-strain response significantl y. The material response predicted by M2 RVE is in good agreement with the experimental results available in the literature. The maximum difference between the shear stress predicted using M2 RVE and the experimental results is ~15% for the bonding strength of 30MPa at the strain value of 1.1%

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

An approximate Kohn-Sham (KS) exchange potential v(xsigma)(CEDA) is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. v(xsigma)(CEDA) is an explicit functional of the occupied KS orbitals, which has the Slater v(Ssigma) and response v(respsigma)(CEDA) potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities \psi(isigma)\(2), as well as "off-diagonal" ones from the occupied-occupied orbital products psi(isigma)psi(j(not equal1)sigma). Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies epsilon(isigma) are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-epsilon(isigma) values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of v(xsigma)(CEDA) appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains H-n over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential. (C) 2002 American Institute of Physics.

Model categories for orthogonal calculus

We restate the notion of orthogonal calculus in terms of model categories. This provides a cleaner set of results and makes the role of O(n)-equivariance clearer. Thus we develop model structures for the category of n-polynomial and n-homogeneous functors, along with Quillen pairs relating them. We then classify n-homogeneous functors, via a zig-zag of Quillen equivalences, in terms of spectra with an O(n)-action. This improves upon the classification theorem of Weiss. As an application, we develop a variant of orthogonal calculus by replacing topological spaces with orthogonal spectra.

Stability Analysis and Implementation of a Decentralized Formation Control Strategy for Unmanned Vehicles

This paper presents a new methodology for solving the multi-vehicle formation control problem. It employs a unique extension-decomposition-aggregation scheme to transform the overall complex formation control problem into a group of subproblems, which work via boundary interactions or disturbances. Thus, it is proved that the overall formation system is exponentially stable in the sense of Lyapunov, if all the individual augmented subsystems (IASs) are stable. Linear matrix inequality-based H8 control methodology is employed to design the decentralized formation controllers to reject the impact of the formation changes being treated as boundary disturbances and guarantee the stability of all the IASs, consequently maintaining the stability of the overall formation system. Simulation studies are performed to verify the stability, performance, and effectiveness of the proposed strategy.

Interaction-induced correlations and non-Markovianity of quantum dynamics

We investigate the conditions under which the trace distance between two different states of a given open system increases in time due to the interaction with an environment, therefore signaling non-Markovianity. We find that the finite-time difference in trace distance is bounded by two sharply defined quantities that are strictly linked to the occurrence of system-environment correlations created throughout their interaction and affecting the subsequent evolution of the system. This allows us to shed light on the origin of non-Markovian behaviors in quantum dynamics. We best illustrate our findings by tackling two physically relevant examples: a non-Markovian dephasing mechanism that has been the focus of a recent experimental endeavor and the open-system dynamics experienced by a spin connected to a finite-size quantum spin chain.