Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200

Echocardiographic predictors of early in-hospital heart failure during first ST-elevation acute myocardial infarction: does myocardial performance index and left atrial volume improve diagnosis over conventional parameters of left ventricular function?

<p>Abstract</p> <p>Background</p> <p>Left ventricular ejection fraction (LVEF) has been considered a major determinant of early outcome in acute myocardial infarction (AMI). Myocardial performance index (MPI) has been associated to early evolution in AMI in a heterogeneous population, including non ST-elevation or previous AMI. Left atrial volume has been related with late evolution after AMI. We evaluated the independent role of clinical and echocardiographic variables including LVEF, MPI and left atrial volume in predicting early in-hospital congestive heart failure (CHF) specifically in patients with a first isolated ST-elevation AMI.</p> <p>Methods</p> <p>Echocardiography was performed within 30 hours of chest pain in 95 patients with a first ST-elevation AMI followed during the first week of hospitalization. Several clinical and echocardiographic variables were analyzed. CHF was defined as Killip class ≥ II. Multivariate regression analysis was used to select independent predictor of in-hospital CHF.</p> <p>Results</p> <p>Early in-hospital CHF occurred in 29 (31%) of patients. LVEF ≤ 0.45 was the single independent and highly significant predictor of early CHF among other clinical and echocardiographic variables (odds ratio 17.0; [95% CI 4.1 - 70.8]; p < 0.0001). MPI alone could not predict CHF in first ST-elevation AMI patients. Left atrial volume was not associated with early CHF in such patients.</p> <p>Conclusion</p> <p>For patients with first, isolated ST-elevation AMI, LVEF assessed by echocardiography still constitutes a strong and accurate independent predictor of early in-hospital CHF, superior to isolated MPI and left atrial volume in this particular subset of patients.</p

A novel insertion mutation in the cartilage-derived morphogenetic protein-1 (CDMP1) gene underlies Grebe-type chondrodysplasia in a consanguineous Pakistani family

<p>Abstract</p> <p>Background</p> <p>Grebe-type chondrodysplasia (GCD) is a rare autosomal recessive syndrome characterized by severe acromesomelic limb shortness with non-functional knob like fingers resembling toes. Mutations in the cartilage-derived morphogenetic protein 1 (<it>CDMP1</it>) gene cause Grebe-type chondrodysplasia.</p> <p>Methods</p> <p>Genotyping of six members of a Pakistani family with Grebe-type chondrodysplasia, including two affected and four unaffected individuals, was carried out by using polymorphic microsatellite markers, which are closely linked to <it>CDMP1 </it>locus on chromosome 20q11.22. To screen for a mutation in <it>CDMP1 </it>gene, all of its coding exons and splice junction sites were PCR amplified from genomic DNA of affected and unaffected individuals of the family and sequenced directly in an ABI Prism 310 automated DNA sequencer.</p> <p>Results</p> <p>Genotyping results showed linkage of the family to <it>CDMP1 </it>locus. Sequence analysis of the <it>CDMP1 </it>gene identified a novel four bases insertion mutation (1114insGAGT) in exon 2 of the gene causing frameshift and premature termination of the polypeptide.</p> <p>Conclusion</p> <p>We describe a 4 bp novel insertion mutation in <it>CDMP1 </it>gene in a Pakistani family with Grebe-type chondrodysplasia. Our findings extend the body of evidence that supports the importance of <it>CDMP1 </it>in the development of limbs.</p

Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012

The Chromatin Modifier MSK1/2 Suppresses Endocrine Cell Fates during Mouse Pancreatic Development

Type I diabetes is caused by loss of insulin-secreting beta cells. To identify novel, pharmacologically-targetable histone-modifying proteins that enhance beta cell production from pancreatic progenitors, we performed a screen for histone modifications induced by signal transduction pathways at key pancreatic genes. The screen led us to investigate the temporal dynamics of ser-28 phosphorylated histone H3 (H3S28ph) and its upstream kinases, MSK1 and MSK2 (MSK1/2). H3S28ph and MSK1/2 were enriched at the key endocrine and acinar promoters in E12.5 multipotent pancreatic progenitors. Pharmacological inhibition of MSK1/2 in embryonic pancreatic explants promoted the specification of endocrine fates, including the beta-cell lineage, while depleting acinar fates. Germline knockout of both Msk isoforms caused enhancement of alpha cells and a reduction in acinar differentiation, while monoallelic loss of Msk1 promoted beta cell mass. Our screen of chromatin state dynamics can be applied to other developmental contexts to reveal new pathways and approaches to modulate cell fates

Response perseveration and ventral prefrontal sensitivity to reward and punishment in male problem gamblers and smokers

Pathological gambling (PG) is associated with maladaptive perseverative behavior, but the underlying mechanism and neural circuitry is not completely clear. Here, the hypothesis was tested that PG is characterized by response perseveration and abnormalities in reward and/or punishment sensitivity in the ventral frontostriatal circuit. Executive functioning was assessed to verify if these effects are independent of the dorsal frontostriatal circuit. A group of smokers was also included to examine whether impairments in PG generalize to substance use disorders. Response perseveration and reward/punishment sensitivity were measured with a probabilistic reversal-learning task, in which subjects could win and lose money. Executive functioning was measured with a planning task, the Tower of London. Performance and fMRI data were acquired in 19 problem gamblers, 19 smokers, and 19 healthy controls. Problem gamblers showed severe response perseveration, associated with reduced activation of right ventrolateral prefrontal cortex in response to both monetary gain and loss. Results did not fully generalize to smokers. Planning performance and related activation of the dorsal frontostriatal circuit were intact in both problem gamblers and smokers. PG is related to response perseveration and diminished reward and punishment sensitivity as indicated by hypoactivation of the ventrolateral prefrontal cortex when money is gained and lost. Moreover, intact planning abilities and normal dorsal frontostriatal responsiveness indicate that this deficit is not due to impaired executive functioning. Response perseveration and ventral prefrontal hyporesponsiveness to monetary loss may be markers for maladaptive behavior seen in chemical and nonchemical addictions. © 2009 Nature Publishing Group All rights reserved