609 research outputs found
Leibnizian, Robinsonian, and Boolean Valued Monads
This is an overview of the present-day versions of monadology with some
applications to vector lattices and linear inequalities.Comment: This is a talk prepared for the 20th St. Petersburg Summer Meeting in
Mathematical Analysis, June 24-29, 201
Cauchy, infinitesimals and ghosts of departed quantifiers
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been
interpreted in both a Weierstrassian and Robinson's frameworks. The latter
provides closer proxies for the procedures of the classical masters. Thus,
Leibniz's distinction between assignable and inassignable numbers finds a proxy
in the distinction between standard and nonstandard numbers in Robinson's
framework, while Leibniz's law of homogeneity with the implied notion of
equality up to negligible terms finds a mathematical formalisation in terms of
standard part. It is hard to provide parallel formalisations in a
Weierstrassian framework but scholars since Ishiguro have engaged in a quest
for ghosts of departed quantifiers to provide a Weierstrassian account for
Leibniz's infinitesimals. Euler similarly had notions of equality up to
negligible terms, of which he distinguished two types: geometric and
arithmetic. Euler routinely used product decompositions into a specific
infinite number of factors, and used the binomial formula with an infinite
exponent. Such procedures have immediate hyperfinite analogues in Robinson's
framework, while in a Weierstrassian framework they can only be reinterpreted
by means of paraphrases departing significantly from Euler's own presentation.
Cauchy gives lucid definitions of continuity in terms of infinitesimals that
find ready formalisations in Robinson's framework but scholars working in a
Weierstrassian framework bend over backwards either to claim that Cauchy was
vague or to engage in a quest for ghosts of departed quantifiers in his work.
Cauchy's procedures in the context of his 1853 sum theorem (for series of
continuous functions) are more readily understood from the viewpoint of
Robinson's framework, where one can exploit tools such as the pointwise
definition of the concept of uniform convergence.
Keywords: historiography; infinitesimal; Latin model; butterfly modelComment: 45 pages, published in Mat. Stu
3′-Hydroxymethyl 2′-deoxynucleoside 5′-triphosphates are inhibitors highly specific for reverse transcriptase
AbstractdNTP(3′-OCH3), a 3′-O-methyl derivative of dNTP, is a chain terminator substrate for DNA synthesis catalyzed by AMV reverse transriptase. The enzyme seems to be the only DNA polymerase susceptible to the inhibitor while all the other DNA polymerases tested are fully resistant to the nucleotide analog. The resistant polymerases are: E. coli DNA polymerase I, Klenow's fragment of DNA polymerase I, phage T4 DNA polymerase, calf thymus DNA polymerase α, rat liver DNA polymerase β and calf thymus terminal deoxyribonucleotidyl transferase
Cauchy's infinitesimals, his sum theorem, and foundational paradigms
Cauchy's sum theorem is a prototype of what is today a basic result on the
convergence of a series of functions in undergraduate analysis. We seek to
interpret Cauchy's proof, and discuss the related epistemological questions
involved in comparing distinct interpretive paradigms. Cauchy's proof is often
interpreted in the modern framework of a Weierstrassian paradigm. We analyze
Cauchy's proof closely and show that it finds closer proxies in a different
modern framework.
Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation;
uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc
A triple action CDK4/6-PI3K-BET inhibitor with augmented cancer cell cytotoxicity
National Institutes of Health GM125195, GM135671, CA192656, FD00511
An Acetyl-Methyl Switch Drives a Conformational Change in p53
Individual posttranslational modifications (PTMs) of p53 mediate diverse p53-dependent responses, however much less is known about the combinatorial action of adjacent modifications. Here, we describe crosstalk between the early DNA damage response mark p53K382me2 and the surrounding PTMs that modulate binding of p53 co-factors, including 53BP1 and p300. The 1.8 Å resolution crystal structure of the tandem Tudor domain (TTD) of 53BP1 in complex with p53 peptide acetylated at K381 and dimethylated at K382 (p53K381acK382me2) reveals that the dual PTM induces a conformational change in p53. The α-helical fold of p53K381acK382me2 positions the side chains of R379, K381ac, and K382me2 to interact with TTD concurrently, reinforcing a modular design of double PTM mimetics. Biochemical and NMR analyses show that other surrounding PTMs, including phosphorylation of serine/threonine residues of p53, affect association with TTD. Our findings suggest a novel PTM-driven conformation switch-like mechanism that may regulate p53 interactions with binding partners
Molecular basis for chromatin binding and regulation of MLL5
The human mixed-lineage leukemia 5 (MLL5) protein mediates hematopoietic cell homeostasis, cell cycle, and survival; however, the molecular basis underlying MLL5 activities remains unknown. Here, we show that MLL5 is recruited to gene-rich euchromatic regions via the interaction of its plant homeodomain finger with the histone mark H3K4me3. The 1.48-Å resolution crystal structure of MLL5 plant homeodomain in complex with the H3K4me3 peptide reveals a noncanonical binding mechanism, whereby K4me3 is recognized through a single aromatic residue and an aspartate. The binding induces a unique His–Asp swapping rearrangement mediated by a C-terminal α-helix. Phosphorylation of H3T3 and H3T6 abrogates the association with H3K4me3 in vitro and in vivo, releasing MLL5 from chromatin in mitosis. This regulatory switch is conserved in the Drosophila ortholog of MLL5, UpSET, and suggests the developmental control for targeting of H3K4me3. Together, our findings provide first insights into the molecular basis for the recruitment, exclusion, and regulation of MLL5 at chromatin
Set optimization - a rather short introduction
Recent developments in set optimization are surveyed and extended including
various set relations as well as fundamental constructions of a convex analysis
for set- and vector-valued functions, and duality for set optimization
problems. Extensive sections with bibliographical comments summarize the state
of the art. Applications to vector optimization and financial risk measures are
discussed along with algorithmic approaches to set optimization problems
Methylation of ZNF331 is an independent prognostic marker of colorectal cancer and promotes colorectal cancer growth
Mobile Regulatory Cassettes Mediate Modular Shuffling in T4-Type Phage Genomes
Coliphage phi1, which was isolated for phage therapy in the Republic of Georgia,
is closely related to the T-like myovirus RB49. The ∼275 open reading
frames encoded by each phage have an average level of amino acid identity of
95.8%. RB49 lacks 7 phi1 genes while 10 phi1 genes are missing from RB49. Most
of these unique genes encode functions without known homologs. Many of the
insertion, deletion, and replacement events that distinguish the two phages are
in the hyperplastic regions (HPRs) of their genomes. The HPRs are rich in both
nonessential genes and small regulatory cassettes (promoterearly
stem-loops [PeSLs]) composed of strong σ70-like promoters
and stem-loop structures, which are effective transcription terminators. Modular
shuffling mediated by recombination between PeSLs has caused much of the
sequence divergence between RB49 and phi1. We show that exchanges between nearby
PeSLs can also create small circular DNAs that are apparently encapsidated by
the virus. Such PeSL “mini-circles” may be important vectors
for horizontal gene transfer
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