Efficiently Computing Real Roots of Sparse Polynomials

We propose an efficient algorithm to compute the real roots of a sparse polynomial $f\in\mathbb{R}[x]$ having $k$ non-zero real-valued coefficients. It is assumed that arbitrarily good approximations of the non-zero coefficients are given by means of a coefficient oracle. For a given positive integer $L$, our algorithm returns disjoint disks $\Delta_{1},\ldots,\Delta_{s}\subset\mathbb{C}$, with $s<2k$, centered at the real axis and of radius less than $2^{-L}$ together with positive integers $\mu_{1},\ldots,\mu_{s}$ such that each disk $\Delta_{i}$ contains exactly $\mu_{i}$ roots of $f$ counted with multiplicity. In addition, it is ensured that each real root of $f$ is contained in one of the disks. If $f$ has only simple real roots, our algorithm can also be used to isolate all real roots. The bit complexity of our algorithm is polynomial in $k$ and $\log n$, and near-linear in $L$ and $\tau$, where $2^{-\tau}$ and $2^{\tau}$ constitute lower and upper bounds on the absolute values of the non-zero coefficients of $f$, and $n$ is the degree of $f$. For root isolation, the bit complexity is polynomial in $k$ and $\log n$, and near-linear in $\tau$ and $\log\sigma^{-1}$, where $\sigma$ denotes the separation of the real roots

Laparoscopy Pneumoperitoneum Fuzzy Modeling

Abstract: Gas volume to intra-peritoneal pressure fuzzy modeling for evaluating pneumoperitoneum in videolaparoscopic surgery is proposed in this paper. The proposed approach innovates in using fuzzy logic and fuzzy set theory for evaluating the accuracy of the prognosis value in order to minimize or avoid iatrogenic injuries due to the blind needle puncture. In so doing, it demonstrates the feasibility of fuzzy analysis to contribute to medicine and health care. Fuzzy systems is employed here in synergy with artificial neural network based on backpropaga tion, multilayer perceptron architecture for building up numerical functions. Experimental data employed for analysis were collected in the accomplishment of the pneumoperitoneum in a random population of patients submitted to videolaparoscopic surgeries. Numerical results indicate that the proposed fuzzy mapping for describing the relation from the intra peritoneal pressure measures as function injected gas volumes succeeded in determinining a fuzzy model for this nonlinear system when compared to the statistical model

The halogen and uranium content of sedimentary rocks, tektites, impact glasses, and obsidians

The iodine and uranium concentrations in sedimentary rocks were measured by irradiating the samples in a neutron flux, radiochemically separating iodine, and ß-counting the resulting activity. The values obtained for uranium are in good agreement with previous estimates of the uranium content in sedimentary rocks. The values obtained for iodine define a distribution pattern similar to that reported for chlorine and bromine, in contrast with the distribution pattern previously reported for iodine in sedimentary rocks. The concentrations of chlorine, bromine, iodine and uranium were determined in tektites, obsidians and impact glasses by neutron activation. The uranium content found in tektites is suggestive of an origin from material in the earth\u27s lithosphere. However, the halogen content is lower than that in obsidians or impactites, and lower than the halogen content reported in any terrestrial rocks. It is concluded that severe loss of halogens would be required for the production of tektites from terrestrial material. A similarity observed in the abundance pattern for the halogens in tektites and in impactites is interpreted as evidence that these two glasses could be derived from the same parent material --Abstract, page iii

Assessing Post-ADA Employment: Some Econometric Evidence and Policy Considerations

This article explores the relationship between the Americans with Disabilities Act (“ADA”) and the relative labor market outcomes for people with disabilities. Using individual-level longitudinal data from 1981 to 1996 derived from the previously unexploited Panel Study of Income Dynamics (“PSID”), we examine the possible effect of the ADA on (1) annual weeks worked; (2) annual earnings; and (3) hourly wages for a sample of 7120 unique male household heads between the ages of 21 and 65 as well as a subset of 1437 individuals appearing every year from 1981 to 1996. Our analysis of the larger sample suggests the ADA had a negative impact on the employment levels of disabled persons relative to non-disabled persons but no impact on relative earnings. However, our evaluation of the restricted sample raises questions about these findings. Using these data, we find little evidence of adverse effects on weeks worked but strong evidence of wage declines for the disabled, albeit declines beginning in 1986, well before the ADA’s passage. These results therefore cast doubt on the adverse ADA-related impacts found in previous studies, particularly Acemoglu and Angrist (2001). The conflicting narratives that emerge from our analysis shed new light on, but also counsel caution in reaching final conclusions about, the impact of the ADA on employment outcomes for people with disabilities

Assessing Post-ADA Employment: Some Econometric Evidence and Policy Considerations

This article explores the relationship between the Americans with Disabilities Act (“ADA”) and the relative labor market outcomes for people with disabilities. Using individual-level longitudinal data from 1981 to 1996 derived from the previously unexploited Panel Study of Income Dynamics (“PSID”), we examine the possible effect of the ADA on (1) annual weeks worked; (2) annual earnings; and (3) hourly wages for a sample of 7120 unique male household heads between the ages of 21 and 65 as well as a subset of 1437 individuals appearing every year from 1981 to 1996. Our analysis of the larger sample suggests the ADA had a negative impact on the employment levels of disabled persons relative to non-disabled persons but no impact on relative earnings. However, our evaluation of the restricted sample raises questions about these findings. Using these data, we find little evidence of adverse effects on weeks worked but strong evidence of wage declines for the disabled, albeit declines beginning in 1986, well before the ADA’s passage. These results therefore cast doubt on the adverse ADA-related impacts found in previous studies, particularly Acemoglu and Angrist (2001). The conflicting narratives that emerge from our analysis shed new light on, but also counsel caution in reaching final conclusions about, the impact of the ADA on employment outcomes for people with disabilities

Some reflections on Termination: Transference and Countertransference

INTRODUCTION Nearing the completion of my psychiatric residency, I ingenuously told my supervisor that I needed to know the steps of termination in therapy with patients. On the surface, this request reflected an awareness of the issues at hand and their importance. Beneath lay ambivalence and countertransference anxiety . For the graduating resident, time ordinarily invested in thought and study fills with practical considerations of job hunting and starting a practice. The resident\u27 s own unresolved and unsettling separation issues can further push aside therapeutic considerations for his patients. Termination, the art of the veteran therapist, becomes an unwelcome task at this time of professional passage when anything codifying professional identity is sought. In the unfortunate sequence of most residencies, this can be the first experience with forced termination of therapy. Forced termination is also a neglected topic within termination literature: a stepchild absent from standard psychotherapy texts from Colby to Tarachow. Weigert (1) and many others expound a necessary mutuality between patient and the rapist before termination can be set. Any prematurity on the therapist\u27s part, by definition, sets up a forced situation with its concommitant transference reactions and may be initiated by unintentional countertransference reactions. In reference to character analysis, Freud (2) doubted if even deep analysis could prevent a return of neurotic symptoms under the pressures of everyday life. The issue here becomes not whether treatment is terminable; but rather, one of understanding transference and countertransference. Supervision and the resident\u27s own therapy can make difficult terrain into a crucial learning experience. I share my experience with just one patient and my imperfect understanding of a complex interaction, in light of termination literature

A Synopsis of the 1979 Amendments to the Federal Rules of Criminal Procedure

On April 30, 1979, the Supreme Court of the United States ordered the amendment of the Federal Rules of Criminal Procedure. The modifications ordered by the Court promise to bring about significant changes in the Rules, clarify ambiguous sections, eliminate confusion in application, and bring the Rules into conformity with recent case law. The process of amending the Federal Rules of Criminal Procedure began with the Advisory Committee on Criminal Rules of the Judicial Conference of the United States. The Advisory Committee was responsible for drafting the text of the proposed amendments and submitting explanatory comments. The proposed changes and additions were then sent to the Committee on Rules of Practice and Procedure of the Judicial Conference, which solicited comments from the bench and bar before submitting the amendments to the Judicial Conference. Subsequently, the Judicial Conference approved the proposed amendments and transmitted them to the Supreme Court. The Supreme Court then ordered these amendments to take effect on August 1, 1979. Upon receipt by Congress, the amendments to the Rules were referred to the House Subcommittee on Criminal Justice. Currently engaged in a major effort to overhaul the Federal Criminal Code, the Subcommittee was unable to study the proposed changes in detail. Consequently, the Subcommittee acted to delay the passage of those amendments that it regarded as particularly controversial or far-reaching. Accordingly, Congress delayed the effective dates of the modifications to rules 11(e)(6), 17(h), 32(f), and 44(c) and the enactment of rules 26.2 and 32.1 until a study of the changes could be made, or until December 1, 1980, whichever comes first. This comment will analyze the changes made in the Federal Rules, particularly noting the rationale for the various amendments and the intended effects of those changes