15,992 research outputs found
Compressibility and probabilistic proofs
We consider several examples of probabilistic existence proofs using
compressibility arguments, including some results that involve Lov\'asz local
lemma.Comment: Invited talk for CiE 2017 (full version
PCA and K-Means decipher genome
In this paper, we aim to give a tutorial for undergraduate students studying
statistical methods and/or bioinformatics. The students will learn how data
visualization can help in genomic sequence analysis. Students start with a
fragment of genetic text of a bacterial genome and analyze its structure. By
means of principal component analysis they ``discover'' that the information in
the genome is encoded by non-overlapping triplets. Next, they learn how to find
gene positions. This exercise on PCA and K-Means clustering enables active
study of the basic bioinformatics notions. Appendix 1 contains program listings
that go along with this exercise. Appendix 2 includes 2D PCA plots of triplet
usage in moving frame for a series of bacterial genomes from GC-poor to GC-rich
ones. Animated 3D PCA plots are attached as separate gif files. Topology
(cluster structure) and geometry (mutual positions of clusters) of these plots
depends clearly on GC-content.Comment: 18 pages, with program listings for MatLab, PCA analysis of genomes
and additional animated 3D PCA plot
The Radius of Metric Subregularity
There is a basic paradigm, called here the radius of well-posedness, which
quantifies the "distance" from a given well-posed problem to the set of
ill-posed problems of the same kind. In variational analysis, well-posedness is
often understood as a regularity property, which is usually employed to measure
the effect of perturbations and approximations of a problem on its solutions.
In this paper we focus on evaluating the radius of the property of metric
subregularity which, in contrast to its siblings, metric regularity, strong
regularity and strong subregularity, exhibits a more complicated behavior under
various perturbations. We consider three kinds of perturbations: by Lipschitz
continuous functions, by semismooth functions, and by smooth functions,
obtaining different expressions/bounds for the radius of subregularity, which
involve generalized derivatives of set-valued mappings. We also obtain
different expressions when using either Frobenius or Euclidean norm to measure
the radius. As an application, we evaluate the radius of subregularity of a
general constraint system. Examples illustrate the theoretical findings.Comment: 20 page
On-chip integrated amplifiers and lasers utilizing rare-earth-ion activation
This contribution reviews our recent results on rare-earth-ion-doped integrated amplifiers and lasers. We have concentrated our efforts on complex-doped polymers, amorphous Al2O3, and crystalline potassium double tungstates
Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory
One of the central problems in quantum mechanics is to determine the ground
state properties of a system of electrons interacting via the Coulomb
potential. Since its introduction by Hohenberg, Kohn, and Sham, Density
Functional Theory (DFT) has become the most widely used and successful method
for simulating systems of interacting electrons, making their original work one
of the most cited in physics. In this letter, we show that the field of
computational complexity imposes fundamental limitations on DFT, as an
efficient description of the associated universal functional would allow to
solve any problem in the class QMA (the quantum version of NP) and thus
particularly any problem in NP in polynomial time. This follows from the fact
that finding the ground state energy of the Hubbard model in an external
magnetic field is a hard problem even for a quantum computer, while given the
universal functional it can be computed efficiently using DFT. This provides a
clear illustration how the field of quantum computing is useful even if quantum
computers would never be built.Comment: 8 pages, 3 figures. v2: Version accepted at Nature Physics; differs
significantly from v1 (including new title). Includes an extra appendix (not
contained in the journal version) on the NP-completeness of Hartree-Fock,
which is taken from v
Primary Carcinosarcoma of Ovary an Unusual Tumor Case Report with Review of Literature
Primary ovarian carcinosarcoma is a rare biphasic tumor. There is variable admixture of both malignant epithelial and stromal component seen in this tumor. We report a case of a primary carcinosarcoma of ovary in a 72‑year‑old post‑menopausal female presenting with the complaint of abdominal distension. Staging laparotomy was done for this patient, and final histopathology was reported as the carcinosarcoma of ovary. The epithelial and sarcomatous components showed immunohistochemical positivity for their respective markers.Keywords: Malignant mixed Mullerian tumor, ovary, primary carcinosarcom
Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra
We define a theory of Galilean gravity in 2+1 dimensions with cosmological
constant as a Chern-Simons gauge theory of the doubly-extended Newton-Hooke
group, extending our previous study of classical and quantum gravity in 2+1
dimensions in the Galilean limit. We exhibit an r-matrix which is compatible
with our Chern-Simons action (in a sense to be defined) and show that the
associated bi-algebra structure of the Newton-Hooke Lie algebra is that of the
classical double of the extended Heisenberg algebra. We deduce that, in the
quantisation of the theory according to the combinatorial quantisation
programme, much of the quantum theory is determined by the quantum double of
the extended q-deformed Heisenberg algebra.Comment: 22 page
Preventing leprosy with retrospective active case finding combined with single-dose rifampicin for contacts in a low endemic setting: results of the Leprosy Post-Exposure Prophylaxis program in Cambodia
Post-exposure prophylaxis (PEP) with single-dose rifampicin (SDR) reduces the risk of developing leprosy among contacts of leprosy patients. Most evidence for the feasibility of the intervention is from highly endemic settings while low-endemic areas present unique challenges including reduced awareness of the disease among the population and in the health system, and the only sporadic occurrence of cases which together make defining any type of routine process challenging. We complemented the retrospective active case finding (RACF) approach with SDR administration to eligible contacts, and piloted the intervention across 31 operational districts in Cambodia. The aim was to demonstrate the feasibility of improving early case detection and administering SDR in a low endemic setting. The intervention focused on leprosy patients diagnosed since 2011 and was implemented between October 2016 - September 2019. The "drives" approach was employed to trace contacts: a trained team systematically contacted all eligible cases in a district, traced and screened contacts, and administered SDR. A total of 555 index patients were traced by the drive team, and 10,410 contacts in their household and 5 immediate neighbor houses listed. Among these contacts, 72.0% could be screened while most others were absent on the screening day. A total of 33 new leprosy cases were diagnosed and 6189 contacts received SDR (82.6% of the screened contacts). Sixty-one contacts refused SDR administration. We conclude that integrating PEP with SDR in RACF campaigns is feasible, and that this approach is appropriate in low resource and low endemic settings. Over time, evidence on whether or not the approach reduced leprosy transmission in Cambodia, may become clear
Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity
In this work we investigate the canonical quantization of 2+1 gravity with
cosmological constant in the canonical framework of loop quantum
gravity. The unconstrained phase space of gravity in 2+1 dimensions is
coordinatized by an SU(2) connection and the canonically conjugate triad
field . A natural regularization of the constraints of 2+1 gravity can be
defined in terms of the holonomies of . As a first step
towards the quantization of these constraints we study the canonical
quantization of the holonomy of the connection on the
kinematical Hilbert space of loop quantum gravity. The holonomy operator
associated to a given path acts non trivially on spin network links that are
transversal to the path (a crossing). We provide an explicit construction of
the quantum holonomy operator. In particular, we exhibit a close relationship
between the action of the quantum holonomy at a crossing and Kauffman's
q-deformed crossing identity. The crucial difference is that (being an operator
acting on the kinematical Hilbert space of LQG) the result is completely
described in terms of standard SU(2) spin network states (in contrast to
q-deformed spin networks in Kauffman's identity). We discuss the possible
implications of our result.Comment: 19 pages, references added. Published versio
Assessment of ROS Production in the Mitochondria of Live Cells
Production of reactive oxygen species (ROS) in the mitochondria plays multiple roles in physiology, and excessive production of ROS leads to the development of various pathologies. ROS in the mitochondria are generated by various enzymes, mainly in the electron transporvt chain, and it is important to identify not only the trigger but also the source of free radical production. It is important to measure mitochondrial ROS in live, intact cells, because activation of ROS production could be initiated by changes in extramitochondrial processes which could be overseen when using isolated mitochondria. Here we describe the approaches, which allow to measure production of ROS in the matrix of mitochondria in live cells. We also demonstrate how to measure kinetic changes in lipid peroxidation in mitochondria of live cells. These methods could be used for understanding the mechanisms of pathology in a variety of disease models and also for testing neuro- or cardioprotective chemicals
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