A Quasi-Random Approach to Matrix Spectral Analysis

Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of Hermitian matrices. The result is a completely new, efficient and stable, parallel algorithm to compute an approximate spectral decomposition of any Hermitian matrix. The algorithm can be implemented by Boolean circuits in $O(\log^2 n)$ parallel time with a total cost of $O(n^{\omega+1})$ Boolean operations. This Boolean complexity matches the best known rigorous $O(\log^2 n)$ parallel time algorithms, but unlike those algorithms our algorithm is (logarithmically) stable, so further improvements may lead to practical implementations. All previous efficient and rigorous approaches to solve the Eigen-Problem use randomization to avoid bad condition as we do too. Our algorithm makes further use of randomization in a completely new way, taking random powers of a unitary matrix to randomize the phases of its eigenvalues. Proving that a tiny Gaussian perturbation and a random polynomial power are sufficient to ensure almost pairwise independence of the phases $(\mod (2\pi))$ is the main technical contribution of this work. This randomization enables us, given a Hermitian matrix with well separated eigenvalues, to sample a random eigenvalue and produce an approximate eigenvector in $O(\log^2 n)$ parallel time and $O(n^\omega)$ Boolean complexity. We conjecture that further improvements of our method can provide a stable solution to the full approximate spectral decomposition problem with complexity similar to the complexity (up to a logarithmic factor) of sampling a single eigenvector.Comment: Replacing previous version: parallel algorithm runs in total complexity $n^{\omega+1}$ and not $n^{\omega}$. However, the depth of the implementing circuit is $\log^2(n)$: hence comparable to fastest eigen-decomposition algorithms know

Prognostication after out-of-hospital cardiac arrest, a clinical survey

Background: Numerous parameters and tests have been proposed for outcome prediction in comatose out-of-hospital cardiac arrest survivors. We conducted a survey of clinical practice of prognostication after therapeutic hypothermia (TH) became common practice in Norway. Methods: By telephone, we interviewed the consultants who were in charge of the 25 ICUs admitting cardiac patients using 6 structured questions regarding timing, tests used and medical specialties involved in prognostication, as well as the clinical importance of the different parameters used and the application of TH in these patients. Results: Prognostication was conducted within 24–48 hours in the majority (72%) of the participating ICUs. The most commonly applied parameters and tests were a clinical neurological examination (100%), prehospital data (76%), CCT (56%) and EEG (52%). The parameters and tests considered to be of greatest importance for accurate prognostication were prehospital data (56%), neurological examination (52%), and EEG (20%). In 76% of the ICUs, a multidisciplinary approach to prognostication was applied, but only one ICU used a standardised protocol. Therapeutic hypothermia was in routine use in 80% of the surveyed ICUs. Conclusion: Despite the routine use of TH, outcome prediction was performed early and was mainly based on prehospital information, neurological examination and CCT and EEG evaluation. Somatosensory evoked potentials appear to be underused and underrated, while the importance of prehospital data, CCT and EEG to appear to be overrated as methods for making accurate predictions. More evidence-based protocols for prognostication in cardiac arrest survivors, as well as additional studies on the effect of TH on known prognostic parameters are needed

Successful use of therapeutic hypothermia in an opiate induced out-of-hospital cardiac arrest complicated by severe hypoglycaemia and amphetamine intoxication: a case report

The survival to discharge rate after unwitnessed, non-cardiac out-of-hospital cardiac arrest (OHCA) is dismal. We report the successful use of therapeutic hypothermia in a 26-year old woman with OHCA due to intentional poisoning with heroin, amphetamine and insulin

Functional roles for noise in genetic circuits

The genetic circuits that regulate cellular functions are subject to stochastic fluctuations, or ‘noise’, in the levels of their components. Noise, far from just a nuisance, has begun to be appreciated for its essential role in key cellular activities. Noise functions in both microbial and eukaryotic cells, in multicellular development, and in evolution. It enables coordination of gene expression across large regulons, as well as probabilistic differentiation strategies that function across cell populations. At the longest timescales, noise may facilitate evolutionary transitions. Here we review examples and emerging principles that connect noise, the architecture of the gene circuits in which it is present, and the biological functions it enables. We further indicate some of the important challenges and opportunities going forward

The Case for Behaviorally Informed Regulation

Policymakers approach human behavior largely through the perspective of the “rational agent” model, which relies on normative, a priori analyses of the making of rational decisions. This perspective is promoted in the social sciences and in professional schools, and has come to dominate much of the formulation and conduct of policy. An alternative view, developed mostly through empirical behavioral research, provides a substantially different perspective on individual behavior and its policy implications. Behavior, according to the empirical perspective, is the outcome of perceptions, impulses, and other processes that characterize the impressive machinery that we carry behind the eyes and between the ears. These proclivities, research has shown, intrude upon and shape behavior, often quite independently of deliberative intent, and in contrast with normative ideals that people endorse upon reflection. The results are systematic behaviors that are unforeseen and misunderstood by classical policy thinking. A more nuanced behavioral perspective, such research suggests, can yield deeper understanding and improved regulatory insight

Behaviorally Informed Financial Services Regulation

Financial services decisions can have enourmous consequences for household well-being. Households need a range of financial services - to conduct basic transactions, such as receiving their income, storing it, and paying bills; to save for emergency needs and long-term goals; to access credit; and to insure against life\u27s key risks. But the financial services system is exceedingly complicated and often not well-designed to optimize house-hold behavior. In response to the complexity of out financial system, there has been a long running debate about the appropriate role and form of regulation. Regulation is largely stuck in two competing models - disclosure, and usury or product restrictions. This paper explores a different approach, based on insights from behavioral economics on one hand, and an understanding of industrial organization on the other. At the core of the analysis is the interaction between individual psychology and market competition. This is in contrast to the classic model, which relies on the interaction between rational choice and market competition. The introduction of richer psychology complicates the impact of competition. It helps us understand that firms compete based on how individuals will respond to products in the marketplace, and competitive outcomes may not always and in all contexts closely align with improved decisional choice and increased consumer welfare. This paper adopts a behavioral economic framework that considers firm incentives to respond to regulation. Under this framework, outcomes are an equilibrium interaction between individuals with specific psychologies and firms that responds to those psychologies within specific market contexts. Regulation must then address failures in this equilibrium. The model suggests, for example, that in some contexts market participants seek to overcome common human failings (as for example, with under-saving) while in other contexts market participants seek to exploit those failings (as for example, with over-borrowing). Behaviorally informed regulation needs to take account of these different contexts. The paper discusses the specific application of these forces to the case of mortage, credit card, and banking markets. The purpose of this paper is not to champion politics, but to illustrate how a behaviorally informed regulatory analysis would lead to a deeper understanding of the costs and benefits of specific policies

An Opt-Out Home Mortgage System

The current housing and financial crisis has led to significant congressional and executive action to manage the crisis and stem the harms from it, but the fundamental problems that caused the crisis remain largely unaddressed. The central features of the industrial organization of the mortgage market with its misaligned incentives, and the core psychological and behavioral phenomena that drive household financial decisionmaking remain. While the causes of the mortgage meltdown are myriad and the solutions likely to be multifaceted, a central problem that led to the crisis was that brokers and lenders offered loans that looked much less expensive and much less risky than they really were—and borrowers took them. It is time for common-sense reform to the mortgage market. This paper develops a new framework for understanding the mortgage markets as the interaction between individuals with specific psychological biases and firms that respond to those psychologies within specific markets. We argue that regulation needs to take account of that interaction. Our new framework leads us to propose a sticky opt-out mortgage system, under which lenders would be required to offer borrowers loans with standard terms. Borrowers could opt out for other loans, but only after heightened disclosure requirements, and lenders would face increased exposure to liability or other sanctions

The Case for Behaviorally Informed Regulation

Policymakers approach human behavior largely through the perspective of the “rational agent” model, which relies on normative, a priori analyses of the making of rational decisions. This perspective is promoted in the social sciences and in professional schools, and has come to dominate much of the formulation and conduct of policy. An alternative view, developed mostly through empirical behavioral research, provides a substantially different perspective on individual behavior and its policy implications. Behavior, according to the empirical perspective, is the outcome of perceptions, impulses, and other processes that characterize the impressive machinery that we carry behind the eyes and between the ears. These proclivities, research has shown, intrude upon and shape behavior, often quite independently of deliberative intent, and in contrast with normative ideals that people endorse upon reflection. The results are systematic behaviors that are unforeseen and misunderstood by classical policy thinking. A more nuanced behavioral perspective, such research suggests, can yield deeper understanding and improved regulatory insight