1,413 research outputs found
On the multiplicative complexity of the Discrete Fourier Transform
AbstractMost results in multiplicative complexity assume that the functions to be computed are in the field of constants extended by indeterminates, that is, the variables satisfy no algebraic relation. In this paper we extend some of the known results to the case that some of the variables do satisfy some algebraic relations. We then apply these results to obtaining a lower bound on the multiplicative complexity of the Discrete Fourier Transform. In the special case of computing the Discrete Fourier Transform of a prime number of points, the lower bound is actually attainable
Neurophysiology
Contains reports on three research projects.Bell Telephone Laboratories, IncorporatedNational Institutes of HealthTeagle Foundation, IncorporatedUnited States Air Force (WADD Contract AF33(616)-7783
Polynomial evaluation over finite fields: new algorithms and complexity bounds
An efficient evaluation method is described for polynomials in finite fields.
Its complexity is shown to be lower than that of standard techniques when the
degree of the polynomial is large enough. Applications to the syndrome
computation in the decoding of Reed-Solomon codes are highlighted.Comment: accepted for publication in Applicable Algebra in Engineering,
Communication and Computing. The final publication will be available at
springerlink.com. DOI: 10.1007/s00200-011-0160-
Neurophysiology
Contains reports on four research projects.National Institutes of Health (Grant B-1865-(C3), Grant MH-04737-02)United States Air Force, Aeronautical Systems Division (Contract AF33(616)-7783)Teagle Foundation, IncorporatedBell Telephone Laboratories, Incorporate
Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization
A versatile method is described for the practical computation of the discrete
Fourier transforms (DFT) of a continuous function given by its values
at the points of a uniform grid generated by conjugacy classes
of elements of finite adjoint order in the fundamental region of
compact semisimple Lie groups. The present implementation of the method is for
the groups SU(2), when is reduced to a one-dimensional segment, and for
in multidimensional cases. This simplest case
turns out to result in a transform known as discrete cosine transform (DCT),
which is often considered to be simply a specific type of the standard DFT.
Here we show that the DCT is very different from the standard DFT when the
properties of the continuous extensions of these two discrete transforms from
the discrete grid points to all points are
considered. (A) Unlike the continuous extension of the DFT, the continuous
extension of (the inverse) DCT, called CEDCT, closely approximates
between the grid points . (B) For increasing , the derivative of CEDCT
converges to the derivative of . And (C), for CEDCT the principle of
locality is valid. Finally, we use the continuous extension of 2-dimensional
DCT to illustrate its potential for interpolation, as well as for the data
compression of 2D images.Comment: submitted to JMP on April 3, 2003; still waiting for the referee's
Repor
Patients with serious injection drug use-related infections who experience patient-directed discharges on oral antibiotics have high rates of antibiotic adherence but require multidisciplinary outpatient support for retention in care
Background: Persons who inject drugs (PWID) are frequently admitted for serious injection-related infections (SIRIs). Outcomes and adherence to oral antibiotics for PWID with patient-directed discharge (PDD) remain understudied.
Methods: We conducted a prospective multicenter bundled quality improvement project of PWID with SIRI at 3 hospitals in Missouri. All PWID with SIRI were offered multidisciplinary care while inpatient, including the option of addiction medicine consultation and medications for opioid use disorder (MOUD). All patients were offered oral antibiotics in the event of a PDD either at discharge or immediately after discharge through an infectious diseases telemedicine clinic. Additional support services included health coaches, a therapist, a case manager, free clinic follow-up, and medications in an outpatient bridge program. Patient demographics, comorbidities, 90-day readmissions, and substance use disorder clinic follow-up were compared between PWID with PDD on oral antibiotics and those who completed intravenous (IV) antibiotics using an as-treated approach.
Results: Of 166 PWID with SIRI, 61 completed IV antibiotics inpatient (37%), while 105 had a PDD on oral antibiotics (63%). There was no significant difference in 90-day readmission rates between groups (
Conclusions: PWID with SIRI who experience a PDD should be provided with oral antibiotics. Multidisciplinary outpatient support services are needed for PWID with PDD on oral antibiotics
Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit
We study a generic but simple non-integrable quantum {\em many-body} system
of {\em locally} interacting particles, namely a kicked model of spinless
fermions on 1-dim lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2
spins). Statistical properties of dynamics (quantum ergodicity and quantum
mixing) and the nature of quantum transport in {\em thermodynamic limit} are
considered as the kick parameters (which control the degree of
non-integrability) are varied. We find and demonstrate {\em ballistic}
transport and non-ergodic, non-mixing dynamics (implying infinite conductivity
at all temperatures) in the {\em integrable} regime of zero or very small kick
parameters, and more generally and important, also in {\em non-integrable}
regime of {\em intermediate} values of kicked parameters, whereas only for
sufficiently large kick parameters we recover quantum ergodicity and mixing
implying normal (diffusive) transport. We propose an order parameter (charge
stiffness ) which controls the phase transition from non-mixing/non-ergodic
dynamics (ordered phase, ) to mixing/ergodic dynamics (disordered phase,
D=0) in the thermodynamic limit. Furthermore, we find {\em exponential decay of
time-correlation function} in the regime of mixing dynamics.
The results are obtained consistently within three different numerical and
analytical approaches: (i) time evolution of a finite system and direct
computation of time correlation functions, (ii) full diagonalization of finite
systems and statistical analysis of stationary data, and (iii) algebraic
construction of quantum invariants of motion of an infinite system, in
particular the time averaged observables.Comment: 18 pages in REVTeX with 14 eps figures included, Submitted to
Physical Review
An adaptive prefix-assignment technique for symmetry reduction
This paper presents a technique for symmetry reduction that adaptively
assigns a prefix of variables in a system of constraints so that the generated
prefix-assignments are pairwise nonisomorphic under the action of the symmetry
group of the system. The technique is based on McKay's canonical extension
framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the
technique are (i) adaptability---the prefix sequence can be user-prescribed and
truncated for compatibility with the group of symmetries; (ii)
parallelizability---prefix-assignments can be processed in parallel
independently of each other; (iii) versatility---the method is applicable
whenever the group of symmetries can be concisely represented as the
automorphism group of a vertex-colored graph; and (iv) implementability---the
method can be implemented relying on a canonical labeling map for
vertex-colored graphs as the only nontrivial subroutine. To demonstrate the
practical applicability of our technique, we have prepared an experimental
open-source implementation of the technique and carry out a set of experiments
that demonstrate ability to reduce symmetry on hard instances. Furthermore, we
demonstrate that the implementation effectively parallelizes to compute
clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie
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