485 research outputs found
Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations
We present a formal tool for verification of multivariate nonlinear
inequalities. Our verification method is based on interval arithmetic with
Taylor approximations. Our tool is implemented in the HOL Light proof assistant
and it is capable to verify multivariate nonlinear polynomial and
non-polynomial inequalities on rectangular domains. One of the main features of
our work is an efficient implementation of the verification procedure which can
prove non-trivial high-dimensional inequalities in several seconds. We
developed the verification tool as a part of the Flyspeck project (a formal
proof of the Kepler conjecture). The Flyspeck project includes about 1000
nonlinear inequalities. We successfully tested our method on more than 100
Flyspeck inequalities and estimated that the formal verification procedure is
about 3000 times slower than an informal verification method implemented in
C++. We also describe future work and prospective optimizations for our method.Comment: 15 page
Insulin and Glucagon Impairments in Relation with Islet Cells Morphological Modifications Following Long Term Pancreatic Duct Ligation in the Rabbit â A Model of Non-insulin-dependent Diabete
Plasma levels of glucose, insulin and glucagon were
measured at various time intervals after pancreatic
duct ligation (PDL) in rabbits. Two hyperglycemic
periods were observed: one between 15â90 days
(peak at 30 days of 15.1 ± 1.2mmol/l, p < 0.01), and
the other at 450 days (11.2 ± 0.5 mmol/l, p < 0.02). The
first hyperglycemic episode was significantly correlated
with both hypoinsulinemia (41.8 ± 8pmol/l,
r= â0.94, p < 0.01) and hyperglucagonemia (232 ±
21ng/l, r=0.95, p < 0.01). However, the late hyperglycemic
phase (450 days), which was not accompanied
by hypoinsulinemia, was observed after the
hyperglucagonemia (390 days) produced by abundant
immunostained A-cells giving rise to a 3-fold
increase in pancreatic glucagon stores. The insulin
and glucagon responses to glucose loading at 180,
270 and 450 days reflected the insensitivity of B- and
A-cells to glucose. The PDL rabbit model with
chronic and severe glycemic disorders due to the
predominant role of glucagon mimicked key features
of the NIDDM syndrome secondary to
exocrine disease
Acute hormonal response to glucose, lipids and arginine infusion in overweight cats
In cats, the incidence of obesity and diabetes is increasing, and little is known about specific aspects of the endocrine control of food intake in this species. Recent data suggest that ghrelin has an important role in the control of insulin secretion and vice versa, but this role has never been demonstrated in cats. Here we aimed to improve our understanding about the relationship between insulin, amylin and ghrelin secretion in response to a nutrient load in overweight cats. After a 16h fast, weekly, six overweight male cats underwent randomly one of the four testing sessions: saline, glucose, arginine and TAG. All solutions were isoenergetic and isovolumic, and were injected intravenously as a bolus. Glucose, insulin, acylated ghrelin (AG), amylin and prolactin were assayed in plasma before and 10, 20, 40, 60, 80 and 100min after the nutrient load. A linear mixed-effects model was used to assess the effect of bolus and time on the parameters. A parenteral bolus of glucose or arginine increased insulin and ghrelin concentrations in cats. Except for with the TAG bolus, no suppression of ghrelin was observed. The absence of AG suppression after the intravenous load of arginine and glucose may suggest: (1) that some nutrients do not promote satiation in overweight cats; or that (2) AG may be involved in non-homeostatic consumption mechanisms. However, the role of ghrelin in food reward remains to be assessed in cat
Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq
International audienceThe verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors. Due to the tightness of these bounds and the peculiar structure of approximation errors, such a verification is out of the reach of generic tools such as computer algebra systems. In fact, the inherent difficulty of computing such bounds often mandates a formal proof of them. In this paper, we present a tactic for the Coq proof assistant that is designed to automatically and formally prove bounds on univariate expressions. It is based on a formalization of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions. All the computations are performed inside Coq's logic, in a reflexive setting. This paper also compares our tactic with various existing tools on a large set of examples
Neuropathological and Reelin Deficiencies in the Hippocampal Formation of Rats Exposed to MAM; Differences and Similarities with Schizophrenia
Adult rats exposed to methylazoxymethanol (MAM) at embryonic day 17 (E17) consistently display behavioral characteristics similar to that observed in patients with schizophrenia and replicate neuropathological findings from the prefrontal cortex of psychotic individuals. However, a systematic neuropathological analysis of the hippocampal formation and the thalamus in these rats is lacking. It is also unclear if reelin, a protein consistently associated with schizophrenia and potentially involved in the mechanism of action of MAM, participates in the neuropathological effects of this compound. Therefore, a thorough assessment including cytoarchitectural and neuromorphometric measurements of eleven brain regions was conducted. Numbers of reelin positive cells and reelin expression and methylation levels were also studied.Compared to untreated rats, MAM-exposed animals showed a reduction in the volume of entorhinal cortex, hippocampus and mediodorsal thalamus associated with decreased neuronal soma. The entorhinal cortex also showed laminar disorganization and neuronal clusters. Reelin methylation in the hippocampus was decreased whereas reelin positive neurons and reelin expression were unchanged.Our results indicate that E17-MAM exposure reproduces findings from the hippocampal formation and the mediodorsal thalamus of patients with schizophrenia while providing little support for reelin's involvement. Moreover, these results strongly suggest MAM-treated animals have a diminished neuropil, which likely arises from abnormal neurite formation; this supports a recently proposed pathophysiological hypothesis for schizophrenia
The Kinase Function of MSK1 Regulates BDNF Signaling to CREB and Basal Synaptic Transmission, But Is Not Required for Hippocampal Long-Term Potentiation or Spatial Memory
The later stages of long-term potentiation (LTP) in vitro and spatial memory in vivo are believed to depend upon gene transcription. Accordingly, considerable attempts have been made to identify both the mechanisms by which transcription is regulated and indeed the gene products themselves. Previous studies have shown that deletion of one regulator of transcription, the mitogen- and stress-activated kinase 1 (MSK1), causes an impairment of spatial memory. Given the ability of MSK1 to regulate gene expression via the phosphorylation of cAMP response element binding protein (CREB) at serine 133 (S133), MSK1 is a plausible candidate as a prime regulator of transcription underpinning synaptic plasticity and learning and memory. Indeed, prior work has revealed the necessity for MSK1 in homeostatic and experience-dependent synaptic plasticity. However, using a knock-in kinase-dead mouse mutant of MSK1, the current study demonstrates that, while the kinase function of MSK1 is important in regulating the phosphorylation of CREB at S133 and basal synaptic transmission in hippocampal area CA1, it is not required for metabotropic glutamate receptor-dependent long-term depression (mGluR-LTD), two forms of LTP or several forms of spatial learning in the watermaze. These data indicate that other functions of MSK1, such as a structural role for the whole enzyme, may explain previous observations of a role for MSK1 in learning and memory
Dysembryoplastic neuroepithelial tumor and probable sudden unexplained death in epilepsy: a case report
<p>Abstract</p> <p>Introduction</p> <p>This is the first report of the case of a patient with a natural history of dysembryoplastic neuroepithelial tumor associated with probable sudden unexplained death in epilepsy. These tumors are benign, arising within the supratentorial cortex. Over 100 cases have been reported in the literature since the first description by Daumas-Duport in 1988.</p> <p>Case presentation</p> <p>A 24- year-old Caucasian woman had a long period of intractable complex partial seizures, sometimes with tonic-clonic generalization and neuropsychological abnormalities. Magnetic resonance imaging showed a cortico-subcortical parietal tumor with all the characteristics of these types of tumors. After 14 years of evolution, our patient died suddenly during sleep.</p> <p>Conclusion</p> <p>To the best of our knowledge, this is the first case of probable sudden unexplained death in symptomatic epilepsy due to dysembryoplastic neuroepithelial tumor with natural history. Early and complete excision, with functional studies before and during the surgery, leads to better control of seizures, avoiding neuropsychological changes and the risk of death. Patients with refractory epilepsy should be evaluated for any sleep disorders and should have complete cardiology assessments including electrocardiographic evaluation of cardiac rhythm disturbances.</p
Influences of Excluded Volume of Molecules on Signaling Processes on Biomembrane
We investigate the influences of the excluded volume of molecules on
biochemical reaction processes on 2-dimensional surfaces using a model of
signal transduction processes on biomembranes. We perform simulations of the
2-dimensional cell-based model, which describes the reactions and diffusion of
the receptors, signaling proteins, target proteins, and crowders on the cell
membrane. The signaling proteins are activated by receptors, and these
activated signaling proteins activate target proteins that bind autonomously
from the cytoplasm to the membrane, and unbind from the membrane if activated.
If the target proteins bind frequently, the volume fraction of molecules on the
membrane becomes so large that the excluded volume of the molecules for the
reaction and diffusion dynamics cannot be negligible. We find that such
excluded volume effects of the molecules induce non-trivial variations of the
signal flow, defined as the activation frequency of target proteins, as
follows. With an increase in the binding rate of target proteins, the signal
flow varies by i) monotonically increasing; ii) increasing then decreasing in a
bell-shaped curve; or iii) increasing, decreasing, then increasing in an
S-shaped curve. We further demonstrate that the excluded volume of molecules
influences the hierarchical molecular distributions throughout the reaction
processes. In particular, when the system exhibits a large signal flow, the
signaling proteins tend to surround the receptors to form receptor-signaling
protein clusters, and the target proteins tend to become distributed around
such clusters. To explain these phenomena, we analyze the stochastic model of
the local motions of molecules around the receptor.Comment: 31 pages, 10 figure
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