The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

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

The Impact of the COVID-19 Pandemic on First-Generation Women Test-Takers: Magnifying Adversities, Stress, and Consequences for Bar Exam Performance.

By magnifying gender- and socioeconomic status-based inequalities, the COVID-19 pandemic caused stress and disrupted career progress for professional students. The present work investigated the impact of pandemic-related stress and prevailing barriers on structurally disadvantaged women preparing for a high-stakes professional exam. In Study 1, we found that among US law students preparing for the October 2020 California Bar Exam—the professional exam that enables one to become a practicing attorney in California—first-generation women reported the greatest stress from pandemic-related burdens and underperformed on the exam relative to others overall, and particularly compared to continuing-generation women. This underperformance was explained by pandemic-related stress they contended with most, as well as by structural demands shouldered most by first-generation test-takers regardless of gender. Even when controlling for the structural features of caregiving and working while studying, the psychological burdens experienced most by first-generation women predicted lower exam success. Study 2 investigated the February 2021 California Bar Exam. Consistent with Study 1, first-generation women test-takers reported the most pandemic-related stress, which predicted lower exam performance above and beyond structural barriers to exam success. We offer policy prescriptions to bolster the success of at-risk groups in the legal profession pipeline, a challenge magnified by the pandemic

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

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

The response of perennial and temporary headwater stream invertebrate communities to hydrological extremes

The headwaters of karst rivers experience considerable hydrological variability, including spates and streambed drying. Extreme summer flooding on the River Lathkill (Derbyshire, UK) provided the opportunity to examine the invertebrate community response to unseasonal spate flows, flow recession and, at temporary sites, streambed drying. Invertebrates were sampled at sites with differing flow permanence regimes during and after the spates. Following streambed drying at temporary sites, dewatered surface sediments were investigated as a refugium for aquatic invertebrates. Experimental rehydration of these dewatered sediments was conducted to promote development of desiccation-tolerant life stages. At perennial sites, spate flows reduced invertebrate abundance and diversity, whilst at temporary sites, flow reactivation facilitated rapid colonisation of the surface channel by a limited number of invertebrate taxa. Following streambed drying, 38 taxa were recorded from the dewatered and rehydrated sediments, with Oligochaeta being the most abundant taxon and Chironomidae (Diptera) the most diverse. Experimental rehydration of dewatered sediments revealed the presence of additional taxa, including Stenophylax sp. (Trichoptera: Limnephilidae) and Nemoura sp. (Plecoptera: Nemouridae). The influence of flow permanence on invertebrate community composition was apparent despite the aseasonal high-magnitude flood events

Four lectures on secant varieties

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhause

Combining Optimal Control Theory and Molecular Dynamics for Protein Folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the atoms. In turn, MD simulation provides an all-atom conformation whose positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization - MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages