75 research outputs found
Persistence of a Rouse polymer chain under transverse shear flow
We consider a single Rouse polymer chain in two dimensions in presence of a
transverse shear flow along the direction and calculate the persistence
probability that the coordinate of a bead in the bulk of the chain
does not return to its initial position up to time . We show that the
persistence decays at late times as a power law, with
a nontrivial exponent . The analytical estimate of
obtained using an independent interval approximation is in excellent agreement
with the numerical value .Comment: 6 page
Landau theory of glassy dynamics
An exact solution of a Landau model of an order-disorder transition with
activated critical dynamics is presented. The model describes a funnel-shaped
topography of the order parameter space in which the number of energy lowering
trajectories rapidly diminishes as the ordered ground-state is approached. This
leads to an asymmetry in the effective transition rates which results in a
non-exponential relaxation of the order-parameter fluctuations and a
Vogel-Fulcher-Tammann divergence of the relaxation times, typical of a glass
transition. We argue that the Landau model provides a general framework for
studying glassy dynamics in a variety of systems.Comment: 4 pages, 2 figure
Persistence in nonequilibrium surface growth
Persistence probabilities of the interface height in (1+1)- and
(2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface
growth are studied using kinetic Monte Carlo simulations, with emphasis on
models that belong to the molecular beam epitaxy (MBE) universality class. Both
the initial transient and the long-time steady-state regimes are investigated.
We show that for growth models in the MBE universality class, the nonlinearity
of the underlying dynamical equation is clearly reflected in the difference
between the measured values of the positive and negative persistence exponents
in both transient and steady-state regimes. For the MBE universality class, the
positive and negative persistence exponents in the steady-state are found to be
and ,
respectively, in (1+1) dimensions, and and
, respectively, in (2+1) dimensions. The noise
reduction technique is applied on some of the (1+1)-dimensional models in order
to obtain accurate values of the persistence exponents. We show analytically
that a relation between the steady-state persistence exponent and the dynamic
growth exponent, found earlier to be valid for linear models, should be
satisfied by the smaller of the two steady-state persistence exponents in the
nonlinear models. Our numerical results for the persistence exponents are
consistent with this prediction. We also find that the steady-state persistence
exponents can be obtained from simulations over times that are much shorter
than that required for the interface to reach the steady state. The dependence
of the persistence probability on the system size and the sampling time is
shown to be described by a simple scaling form.Comment: 28 pages, 16 figure
Persistence of Randomly Coupled Fluctuating Interfaces
We study the persistence properties in a simple model of two coupled
interfaces characterized by heights h_1 and h_2 respectively, each growing over
a d-dimensional substrate. The first interface evolves independently of the
second and can correspond to any generic growing interface, e.g., of the
Edwards-Wilkinson or of the Kardar-Parisi-Zhang variety. The evolution of h_2,
however, is coupled to h_1 via a quenched random velocity field. In the limit
d\to 0, our model reduces to the Matheron-de Marsily model in two dimensions.
For d=1, our model describes a Rouse polymer chain in two dimensions advected
by a transverse velocity field. We show analytically that after a long waiting
time t_0\to \infty, the stochastic process h_2, at a fixed point in space but
as a function of time, becomes a fractional Brownian motion with a Hurst
exponent, H_2=1-\beta_1/2, where \beta_1 is the growth exponent characterizing
the first interface. The associated persistence exponent is shown to be
\theta_s^2=1-H_2=\beta_1/2. These analytical results are verified by numerical
simulations.Comment: 15 pages, 3 .eps figures include
COMMIPHORA MUKUL EXTRACT AND GUGGULSTERONE EXHIBIT ANTITUMOUR ACTIVITY THROUGH INHIBITION OF CYCLIN D1, NF-Κß AND INDUCTION OF APOPTOSIS IN ORAL CANCER CELLS
ABSTRACTComiphora mukul, a promising medicinal plant and its constituent Guggulsterone (GS) is used in Ayurveda since decades. This study was aimed toinvestigate the anticancer potential of C. mukul and GS on oral cancer cell lines (SCC-4, KB). MTT assay was used to determine tumour cell proliferation,propidium iodide labeling and annexin V- binding, followed by flow cytometry was used to determine cell cycle and apoptosis of tumor cells aftertreatment. Expression of regulatory proteins such as NF-κß, cyclin D1, p53 and vascular endothelial growth factor was determined by western blot.C. mukul and GS significantly inhibited tumor cell growth, caused cell cycle arrest and apoptosis in both tumor cells. Such activities appeared to bedue to inhibition of NF-κß, cyclin D1and restoration of p53. Overall our data suggests that C. mukul and GS may be developed as chemopreventive andchemotherapeutic drug for oral cancer.Keywords: Commiphora mukul, Oral cancer, Antitumor, Cell cycle, Apoptosis, NF-κß, Cyclin D1, P53
Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation
We consider a class of real random polynomials, indexed by an integer d, of
large degree n and focus on the number of real roots of such random
polynomials. The probability that such polynomials have no real root in the
interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is the
exponent associated to the decay of the persistence probability for the
diffusion equation with random initial conditions in space dimension d. For n
even, the probability that such polynomials have no root on the full real axis
decays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for a
physical realization of real random polynomials. We further show that the
probability that such polynomials have exactly k real roots in [0,1] has an
unusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x)
is a universal large deviation function.Comment: 4 pages, 3 figures. Minor changes. Accepted version in Phys. Rev.
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Neuroendocrine Tumor of the Ampulla of Vater: A Case Report
Neuroendocrine tumors (NETs) of the ampulla of Vater are extremely rare. Here, we discuss the clinical presentation, diagnostic challenges, and treatment options of a recently experienced case of NET of the ampulla of Vater in light of the literature. A 56-year-old woman presented with recurrent upper abdominal pain. Ultrasonography (USG) of the whole abdomen showed multiple gallstones along with a dilated common bile duct (CBD). For evaluating the dilated CBD, a magnetic resonance cholangiopancreatography was performed, which revealed the double-duct sign. Subsequently, an upper gastrointestinal endoscopy showed a bulged-out ampulla of the Vater. Biopsy and histopathological examination of the growth yielded the diagnosis of adenocarcinoma. A Whipple procedure was performed. Macroscopically, a 2 cm growth was noted involving the ampulla of Vater, and microscopic findings were consistent with a well-differentiated NET, grade 1 (low grade). The diagnosis was further confirmed by immunohistochemical staining (pan-cytokeratin positive, synaptophysin positive, and focally chromogranin positive). Her postoperative course was uneventful except for delayed gastric emptying. A detailed evaluation and a high index of suspicion are required for the diagnosis of this rare tumor. Treatment is relatively easier after a proper diagnosis
Condensation of the roots of real random polynomials on the real axis
We introduce a family of real random polynomials of degree n whose
coefficients a_k are symmetric independent Gaussian variables with variance
= e^{-k^\alpha}, indexed by a real \alpha \geq 0. We compute exactly
the mean number of real roots for large n. As \alpha is varied, one finds
three different phases. First, for 0 \leq \alpha \sim
(\frac{2}{\pi}) \log{n}. For 1 < \alpha < 2, there is an intermediate phase
where grows algebraically with a continuously varying exponent,
\sim \frac{2}{\pi} \sqrt{\frac{\alpha-1}{\alpha}} n^{\alpha/2}. And finally for
\alpha > 2, one finds a third phase where \sim n. This family of real
random polynomials thus exhibits a condensation of their roots on the real line
in the sense that, for large n, a finite fraction of their roots /n are
real. This condensation occurs via a localization of the real roots around the
values \pm \exp{[\frac{\alpha}{2}(k+{1/2})^{\alpha-1} ]}, 1 \ll k \leq n.Comment: 13 pages, 2 figure
Can an Amino Acid Mixture Alleviate Gastrointestinal Symptoms in Neuroendocrine Tumor Patients?
Background: Neuroendocrine tumors, although relatively rare in incidence, are now the second most prevalent gastrointestinal neoplasm owing to indolent disease biology. A small but significant sub-group of neuroendocrine tumor patients suffer from diarrhea. This is usually secondary to carcinoid syndrome but can also be a result of short gut syndrome, bile acid excess or iatrogenic etiologies. Recently, an amino acid based oral rehydration solution (enterade® Advanced Oncology Formula) was found to have anti-diarrheal properties in preclinical models.
Methods: A retrospective chart review of all NET patients treated with enterade® AO was performed after IRB approval.
Results: Ninety-eight NET patients who had received enterade® AO at our clinic from May 2017 through June 2019 were included. Patients (N = 49 of 98) with follow up data on bowel movements (BMs) were included for final analysis. Eighty-four percent of patients (41/49) had fewer BMs after taking enterade® AO and 66% (27/41) reported more than 50% reduction in BM frequency. The mean number of daily BMs was 6.6 (range, 3–20) at baseline before initiation of therapy, while the mean number of BMs at 1 week time point post enterade® AO was 2.9 (range, 0–11).
Conclusions: Our retrospective observations are encouraging and support prospective validation with appropriate controls in NET patients. This is first published report of the potential anti-diarrheal activity of enterade® AO in NET patients
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