A Simple Method for Organizing Nearly Optimal Binary Search Trees

Improving the efficiency of retrieving information concerns users of computer systems involved in many applications- One way of addressing this concern is to organize a sorted sequence into a binary search tree. Knuth\u27s Algorithm K is a bottom-up organization algorithm that always constructs a binary tree which minimizes average search time. However, the cost of executing Algorithm K is prohibitive for a large tree. The aim of this work is to find a less costly method of organizing sorted sequences into nearly-optimal binary search trees. We present a top-down organization method which yields better average search times than top-down methods already available, specifically height-balancing and weight-balancing. The variation in access frequency among the members of a sequence is used to recommend specific values for some of the parameters in this new method of organization. The new method improves considerably on the cost of organization as opposed to the cost of using Algorithm K while producing trees whose average search times are close to minimal. The new algorithm yields an average search time that is usually within 1% of the minimal average search time and for every case attempted has been no worse than 1.5% larger than minimal

Fermion loops, loop cancellation and density correlations in two dimensional Fermi systems

We derive explicit results for fermion loops with an arbitrary number of density vertices in two dimensions at zero temperature. The 3-loop is an elementary function of the three external momenta and frequencies, and the N-loop can be expressed as a linear combination of 3-loops with coefficients that are rational functions of momenta and frequencies. We show that the divergencies of single loops for low energy and small momenta cancel each other when loops with permuted external variables are summed. The symmetrized N-loop, i.e. the connected N-point density correlation function of the Fermi gas, does not diverge for low energies and small momenta. In the dynamical limit, where momenta scale to zero at fixed finite energy variables, the symmetrized N-loop vanishes as the (2N-2)-th power of the scale parameter.Comment: 24 pages (including 3 EPS figures), LaTeX2e; submitted to Phys. Rev.

Self-Injurious Behaviors in Prisons: A Nationwide Survey of Correctional Mental Health Directors

Self-injurious behavior (SIB) by inmates has serious health, safety, operational, security and fiscal consequences. Serious incidents require a freeze in normal facility operations. Injuries that need outside medical attention create additional security risks, including potential escape attempts. The interruption of normal operations, diversion of staff, cost of outside care, and drain on medical and mental health resources all have significant fiscal consequences. This session will present the results and implications of a survey of the Mental Health Directors in all 51 state and federal prison systems on the extent of SIB by inmates, including incidence and prevalence, adverse consequences, and management. Thirty-nine of the state and federal correctional systems (77%) responded to the survey. Fewer than 2% of inmates per year engage in SIB, but in 29 85%) of systems these events occur at least weekly to more than once per day. The highest rates of occurrence of these behaviors are in maximum security and lock-down units, and most often involve inmates with Axis II disorders. Despite the seriousness of the problem, systems typically collect little, if any, data on self-injurious behaviors, and management approaches lack widespread consistency

THE DENTISTS AND THE SERVICES THEY PROVIDED FOR TWO POPULATIONS; COMMENTS ON METHODOLOGY OF STUDY

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65469/1/j.1752-7325.1965.tb00460.x.pd

Hole dynamics in generalized spin backgrounds in infinite dimensions

We calculate the dynamical behaviour of a hole in various spin backgrounds in infinite dimensions, where it can be determined exactly. We consider hypercubic lattices with two different types of spin backgrounds. On one hand we study an ensemble of spin configurations with an arbitrary spin probability on each sublattice. This model corresponds to a thermal average over all spin configurations in the presence of staggered or uniform magnetic fields. On the other hand we consider a definite spin state characterized by the angle between the spins on different sublattices, i.e a classical spin system in an external magnetic field. When spin fluctuations are considered, this model describes the physics of unpaired particles in strong coupling superconductors.Comment: Accepted in Phys. Rev. B. 18 pages of text (1 fig. included) in Latex + 2 figures in uuencoded form containing the 2 postscripts (mailed separately

Coexistence of solutions in dynamical mean-field theory of the Mott transition

In this paper, I discuss the finite-temperature metal-insulator transition of the paramagnetic Hubbard model within dynamical mean-field theory. I show that coexisting solutions, the hallmark of such a transition, can be obtained in a consistent way both from Quantum Monte Carlo (QMC) simulations and from the Exact Diagonalization method. I pay special attention to discretization errors within QMC. These errors explain why it is difficult to obtain the solutions by QMC close to the boundaries of the coexistence region.Comment: 3 pages, 2 figures, RevTe

Many-body position operator in lattice fermionic systems with periodic boundary conditions

A total position operator $X$ in the position representation is derived for lattice fermionic systems with periodic boundary conditions. The operator is shown to be Hermitian, the generator of translations in momentum space, and its time derivative is shown to correspond to the total current operator in a periodic system. The operator is such that its moments can be calculated up to any order. To demonstrate its utility finite size scaling is applied to the Brinkman-Rice transition as well as metallic and insulating Gutzwiller wavefunctions.Comment: to appear in Journal of Physics A: Mathematical and General (reference will be added later

Equivalence of the Falicov-Kimball and Brandt-Mielsch forms for the free energy of the infinite-dimensional Falicov-Kimball model

Falicov and Kimball proposed a real-axis form for the free energy of the Falicov-Kimball model that was modified for the coherent potential approximation by Plischke. Brandt and Mielsch proposed an imaginary-axis form for the free energy of the dynamical mean field theory solution of the Falicov-Kimball model. It has long been known that these two formulae are numerically equal to each other; an explicit derivation showing this equivalence is presented here.Comment: 4 pages, 1 figure, typeset with ReVTe

Spinless Two-Band Model in Infinite Dimensions

A spinless two-band model is studied in infinite dimension limit. Starting from the atomic limit, the formal exact solution of the model is obtained by means a perturbative treatment of the hopping and hybridisation terms. The model is solved in closed form in high dimensions assuming no local spin fluctuations. The non-Fermi liquid properties appearing in the metallic phase are analysed through the behaviour of the density of states and the self-energy near the Fermi level.Comment: 4 pages, 3 figures, to appear in PRB-Breif Repor

<i>‘What retention’ means to me</i>: the position of the adult learner in student retention

Studies of student retention and progression overwhelmingly appear adopt definitions that place the institution, rather than the student, at the centre. Retention is most often conceived in terms of linear and continuous progress between institutionally identified start and end points. This paper reports on research that considered data from 38 in-depth interviews conducted with individuals who had characteristics often associated with non-traditional engagement in higher education who between 2006 and 2010 had studied an ‘Introduction to HE’ module at one distance higher education institution, some of whom had progressed to further study at that institution, some of whom had not. The research deployed a life histories approach to seek a finer grained understanding of how individuals conceptualise their own learning journey and experience, in order to reflect on institutional conceptions of student retention. The findings highlight potential anomalies hidden within institutional retention rates – large proportions of the interview participants who were not ‘retained’ by the institution reported successful progression to and in other learning institutions and environments, both formal and informal. Nearly all described positive perspectives on lifelong learning which were either engendered or improved by the learning undertaken. This attests to the complexity of individuals’ lives and provides clear evidence that institution-centric definitions of retention and progression are insufficient to create truly meaningful understanding of successful individual learning journeys and experiences. It is argued that only through careful consideration of the lived experience of students and a re-conception of measures of retention, will we be able to offer real insight into improving student retention