Glassy Dynamics of Protein Folding

A coarse grained model of a random polypeptide chain, with only discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues is shown to display stretched exponential relaxation under Metropolis dynamics at low temperatures with the exponent $\beta\simeq 1/4$, in agreement with the best experimental results. The time dependent correlation functions for fluctuations about the native state, computed in the Gaussian approximation for real proteins, have also been found to have the same functional form. Our results indicate that the energy landscape exhibits universal features over a very large range of energies and is relatively independent of the specific dynamics.Comment: RevTeX, 4 pages, multicolumn, including 5 figures; larger computations performed, error bars improve

GaN directional couplers for integrated quantum photonics

Large cross-section GaN waveguides are proposed as a suitable architecture to achieve integrated quantum photonic circuits. Directional couplers with this geometry have been designed with aid of the beam propagation method and fabricated using inductively coupled plasma etching. Scanning electron microscopy inspection shows high quality facets for end coupling and a well defined gap between rib pairs in the coupling region. Optical characterization at 800 nm shows single-mode operation and coupling-length-dependent splitting ratios. Two photon interference of degenerate photon pairs has been observed in the directional coupler by measurement of the Hong-Ou-Mandel dip with 96% visibility.Comment: 4 pages, 5 figure

Examining the California Cut Score: An Empirical Analysis of Minimum Competency, Public Protection, Disparate Impact, and National Standards

The selection of a minimum bar exam passing score (“cut score”) shapes the representation of racial and ethnic minorities in the legal profession and the quality of access to justice in the state. California and national policy makers have not had the benefit of detailed exam performance data that analyzes the effect of the cut score on race and ethnicity. Because policy makers consider the cut score an important public protection mechanism, this study also explored whether the selection of higher cut scores better protected the public from attorneys who do not have the minimum competence to practice law. To conduct the analysis, the study used two data sets. The first data set included 85,727 examinees who sat for 21 administrations of the CBX from 2009-18 and the race and ethnicity of each examinee. The second data set included the ABA discipline data from up to 48 U.S. jurisdictions from 2013-18 and the cut scores in each jurisdiction. Using the first data set,the study determined how the selection of a minimum cut score (1) widens or narrows the racial and ethnic impacts of the bar exam and/or (2) alters the racial and ethnic composition of new attorneys joining the legal profession. Both historical actual and simulated cut scores were analyzed. Using the second data set, this study examined a third factor: the relationship, if any, between minimum cut scores and rates of attorney discipline. This analysis determined that initial and eventual passing rates differed significantly between racial and ethnic groups, and this gap was wider at higher simulated cut scores. A simulation analysis using actual examinee scores confirmed that selecting a lower cut score would have significantly narrowed the achievement gap between Whites and racial and ethnic minorities and would have increased the number of newly admitted minority attorneys in California. For example, at 1440, the achievement gap between Whites and Blacks was 27.4 percentage points. But at a simulated cut score of 1300, the achievement gap between these two groups would have been only 14.5 percentage points. This 12.9 percentage point difference in the achievement gap at 1440 and 1300 demonstrates a disparate effect of the higher cut scores. Using the second data set about disciplinary statistics, the study determined that no relationship exists between the selection of a cut score and the number of complaints, formal charges, or disciplinary actions taken against attorneys in the jurisdictions studied. California’s recent decision to lower the cut score from 1440 to 1390 moved California from having the second-highest cut score to the fourth-highest cut score in the country. However, the report data established that at 1390 California will continue to produce significantly disparate pass rates on the basis of race and ethnicity when compared to the national norm of 1350, the New York standard of 1330, and the simulated model of 1300. This study establishes that maintaining a high cut score does not result in greater public protection as measured by disciplinary statistics but does result in excluding minorities from admission to the bar and the practice of law at rates disproportionately higher than Whites

Tight Kernel Bounds for Problems on Graphs with Small Degeneracy

In this paper we consider kernelization for problems on d-degenerate graphs, i.e. graphs such that any subgraph contains a vertex of degree at most $d$. This graph class generalizes many classes of graphs for which effective kernelization is known to exist, e.g. planar graphs, H-minor free graphs, and H-topological-minor free graphs. We show that for several natural problems on d-degenerate graphs the best known kernelization upper bounds are essentially tight.Comment: Full version of ESA 201

A Many-body Problem with Point Interactions on Two Dimensional Manifolds

A non-perturbative renormalization of a many-body problem, where non-relativistic bosons living on a two dimensional Riemannian manifold interact with each other via the two-body Dirac delta potential, is given by the help of the heat kernel defined on the manifold. After this renormalization procedure, the resolvent becomes a well-defined operator expressed in terms of an operator (called principal operator) which includes all the information about the spectrum. Then, the ground state energy is found in the mean field approximation and we prove that it grows exponentially with the number of bosons. The renormalization group equation (or Callan-Symanzik equation) for the principal operator of the model is derived and the $\beta$ function is exactly calculated for the general case, which includes all particle numbers.Comment: 28 pages; typos are corrected, three figures are adde

The Incremental Garbage Collection of Processes

Key Words and Phrases: garbage collection, multiprocessing systems, processor scheduling. "lazy evaluation, "eager" evaluation. CR Categories: 3.60, 3.80, 4.13, 4.22, 4.32. This report describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-75-C-0522. This paper was presented at the AI*PL Conference at Rochester, N.Y. in August, 1977.This paper investigates some problems associated with an argument evaluation order that we call "future" order, which is different from both call-by-name and call-by-value. In call-by-future, each formal parameter of a function is bound to a separate process (called a "future") dedicated to the evaluation of the corresponding argument. This mechanism allows the fully parallel evaluation of arguments to a function, and has been shown to augment the expressive power of a language. We discuss an approach to a problem that arises in this context: futures which were thought to be relevant when they were created become irrelevant through being ignored in the body of the expression where they were bound. The problem of irrelevant processes also appears in multiprocessing problem-solving systems which start several processors working on the same problem but with different methods, and return with the solution which finishes first. This parallel method strategy has the drawback that the processes which are investigating the losing methods must be identified, stopped, and re-assigned to more useful tasks. The solution we propose is that of garbage collection. We propose that the goal structure of the solution plan be explicitly represented in memory as part of the graph memory (like Lisp's heap) so that a garbage collection algorithm can discover which processes are performing useful work, and which can be recycled for a new task. An incremental algorithm for the unified garbage collection of storage and processes is described.MIT Artificial Intelligence Laboratory Department of Defense Advanced Research Projects Agenc

Tube Models for Rubber-Elastic Systems

In the first part of the paper we show that the constraining potentials introduced to mimic entanglement effects in Edwards' tube model and Flory's constrained junction model are diagonal in the generalized Rouse modes of the corresponding phantom network. As a consequence, both models can formally be solved exactly for arbitrary connectivity using the recently introduced constrained mode model. In the second part, we solve a double tube model for the confinement of long paths in polymer networks which is partially due to crosslinking and partially due to entanglements. Our model describes a non-trivial crossover between the Warner-Edwards and the Heinrich-Straube tube models. We present results for the macroscopic elastic properties as well as for the microscopic deformations including structure factors.Comment: 15 pages, 8 figures, Macromolecules in pres

Conformations of Proteins in Equilibrium

We introduce a simple theoretical approach for an equilibrium study of proteins with known native state structures. We test our approach with results on well-studied globular proteins, Chymotrypsin Inhibitor (2ci2), Barnase and the alpha spectrin SH3 domain and present evidence for a hierarchical onset of order on lowering the temperature with significant organization at the local level even at high temperatures. A further application to the folding process of HIV-1 protease shows that the model can be reliably used to identify key folding sites that are responsible for the development of drug resistance .Comment: 6 pages, 3 eps figure