Formalizing Mathematical Knowledge as a Biform Theory Graph: A Case Study

A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory graph is a network of theories connected by meaning-preserving theory morphisms that map the formulas of one theory to the formulas of another theory. Theory graphs are in turn well suited for formalizing mathematical knowledge at the most convenient level of abstraction using the most convenient vocabulary. We are interested in the problem of whether a body of mathematical knowledge can be effectively formalized as a theory graph of biform theories. As a test case, we look at the graph of theories encoding natural number arithmetic. We used two different formalisms to do this, which we describe and compare. The first is realized in ${\rm CTT}_{\rm uqe}$, a version of Church's type theory with quotation and evaluation, and the second is realized in Agda, a dependently typed programming language.Comment: 43 pages; published without appendices in: H. Geuvers et al., eds, Intelligent Computer Mathematics (CICM 2017), Lecture Notes in Computer Science, Vol. 10383, pp. 9-24, Springer, 201

A Reporter Screen in a Human Haploid Cell Line Identifies CYLD as a Constitutive Inhibitor of NF-κB

The development of forward genetic screens in human haploid cells has the potential to transform our understanding of the genetic basis of cellular processes unique to man. So far, this approach has been limited mostly to the identification of genes that mediate cell death in response to a lethal agent, likely due to the ease with which this phenotype can be observed. Here, we perform the first reporter screen in the near-haploid KBM7 cell line to identify constitutive inhibitors of NF-κB. CYLD was the only currently known negative regulator of NF-κB to be identified, thus uniquely distinguishing this gene. Also identified were three genes with no previous known connection to NF-κB. Our results demonstrate that reporter screens in haploid human cells can be applied to investigate the many complex signaling pathways that converge upon transcription factors

Interpreting Attoclock Measurements of Tunnelling Times

Resolving in time the dynamics of light absorption by atoms and molecules, and the electronic rearrangement this induces, is among the most challenging goals of attosecond spectroscopy. The attoclock is an elegant approach to this problem, which encodes ionization times in the strong-field regime. However, the accurate reconstruction of these times from experimental data presents a formidable theoretical challenge. Here, we solve this problem by combining analytical theory with ab-initio numerical simulations. We apply our theory to numerical attoclock experiments on the hydrogen atom to extract ionization time delays and analyse their nature. Strong field ionization is often viewed as optical tunnelling through the barrier created by the field and the core potential. We show that, in the hydrogen atom, optical tunnelling is instantaneous. By calibrating the attoclock using the hydrogen atom, our method opens the way to identify possible delays associated with multielectron dynamics during strong-field ionization.Comment: 33 pages, 10 figures, 3 appendixe

Identification of host cell factors required for intoxication through use of modified cholera toxin

We describe a novel labeling strategy to site-specifically attach fluorophores, biotin, and proteins to the C terminus of the A1 subunit (CTA1) of cholera toxin (CTx) in an otherwise correctly assembled and active CTx complex. Using a biotinylated N-linked glycosylation reporter peptide attached to CTA1, we provide direct evidence that ∼12% of the internalized CTA1 pool reaches the ER. We also explored the sortase labeling method to attach the catalytic subunit of diphtheria toxin as a toxic warhead to CTA1, thus converting CTx into a cytolethal toxin. This new toxin conjugate enabled us to conduct a genetic screen in human cells, which identified ST3GAL5, SLC35A2, B3GALT4, UGCG, and ELF4 as genes essential for CTx intoxication. The first four encode proteins involved in the synthesis of gangliosides, which are known receptors for CTx. Identification and isolation of the ST3GAL5 and SLC35A2 mutant clonal cells uncover a previously unappreciated differential contribution of gangliosides to intoxication by CTx.Fundação para a Ciência e a Tecnologia (Fellowship

The Type and the Position of HNF1A Mutation Modulate Age at Diagnosis of Diabetes in Patients with Maturity-Onset Diabetes of the Young (MODY)-3

OBJECTIVE—The clinical expression of maturity-onset diabetes of the young (MODY)-3 is highly variable. This may be due to environmental and/or genetic factors, including molecular characteristics of the hepatocyte nuclear factor 1-α (HNF1A) gene mutation. RESEARCH DESIGN AND METHODS—We analyzed the mutations identified in 356 unrelated MODY3 patients, including 118 novel mutations, and searched for correlations between the genotype and age at diagnosis of diabetes. RESULTS—Missense mutations prevailed in the dimerization and DNA-binding domains (74%), while truncating mutations were predominant in the transactivation domain (62%). The majority (83%) of the mutations were located in exons 1- 6, thus affecting the three HNF1A isoforms. Age at diagnosis of diabetes was lower in patients with truncating mutations than in those with missense mutations (18 vs. 22 years, P = 0.005). Missense mutations affecting the dimerization/DNA-binding domains were associated with a lower age at diagnosis than those affecting the transactivation domain (20 vs. 30 years, P = 10−4). Patients with missense mutations affecting the three isoforms were younger at diagnosis than those with missense mutations involving one or two isoforms (P = 0.03). CONCLUSIONS—These data show that part of the variability of the clinical expression in MODY3 patients may be explained by the type and the location of HNF1A mutations. These findings should be considered in studies for the search of additional modifier genetic factors

Runge-Kutta residual distribution schemes

We are concerned with the solution of time-dependent non-linear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge–Kutta-type time-stepping (discretisation in time). The introduced non-linear blending procedure allows us to retain the explicit character of the time-stepping procedure. The resulting methods are second order accurate provided that both spatial and temporal approximations are. The proposed approach results in a global linear system that has to be solved at each time-step. An efficient way of solving this system is also proposed. To test and validate this new framework, we perform extensive numerical experiments on a wide variety of classical problems. An extensive numerical comparison of our approach with other multi-stage residual distribution schemes is also given

MCT1-mediated transport of a toxic molecule is an effective strategy for targeting glycolytic tumors

There is increasing evidence that oncogenic transformation modifies the metabolic program of cells. A common alteration is the upregulation of glycolysis, and efforts to target glycolytic enzymes for anticancer therapy are under way. Here, we performed a genome-wide haploid genetic screen to identify resistance mechanisms to 3-bromopyruvate (3-BrPA), a drug candidate that inhibits glycolysis in a poorly understood fashion. We identified the SLC16A1 gene product, MCT1, as the main determinant of 3-BrPA sensitivity. MCT1 is necessary and sufficient for 3-BrPA uptake by cancer cells. Additionally, SLC16A1 mRNA levels are the best predictor of 3-BrPA sensitivity and are most elevated in glycolytic cancer cells. Furthermore, forced MCT1 expression in 3-BrPA–resistant cancer cells sensitizes tumor xenografts to 3-BrPA treatment in vivo. Our results identify a potential biomarker for 3-BrPA sensitivity and provide proof of concept that the selectivity of cancer-expressed transporters can be exploited for delivering toxic molecules to tumors.National Institutes of Health (U.S.) (NIH CA103866)Jane Coffin Childs Memorial Fund for Medical Research (Fellowship)National Science Foundation (U.S.) (Fellowship)Howard Hughes Medical Institute (Investigator

Induced Charge Fluctuations in Semiconductor Detectors with a Cylindrical Geometry

Now, compound semiconductors are very appealing for hard X-ray room-temperature detectors for medical and astrophysical applications. Despite the attractive properties of compound semiconductors, such as high atomic number, high density, wide band gap, low chemical reactivity and long-term stability, poor hole and electron mobility-lifetime products degrade the energy resolution of these detectors. The main objective of the present study is in development of a mathematical model of the process of the charge induction in a cylindrical geometry with accounting for the charge carrier trapping. The formulae for the moments of the distribution function of the induced charge and the formulae for the mean amplitude and the variance of the signal at the output of the semiconductor detector with a cylindrical geometry were derived. It was shown that the power series expansions of the detector amplitude and the variance in terms of the inverse bias voltage allow determining the Fano factor, electron mobility lifetime product, and the nonuniformity level of the trap density of the semiconductor material

Reversal of aberrant cancer methylome and transcriptome upon direct reprogramming of lung cancer cells

10.1038/srep00592Scientific Reports2