Solvability of Rado systems in D-sets

Rado's Theorem characterizes the systems of homogenous linear equations having the property that for any finite partition of the positive integers one cell contains a solution to these equations. Furstenberg and Weiss proved that solutions to those systems can in fact be found in every central set. (Since one cell of any finite partition is central, this generalizes Rado's Theorem.) We show that the same holds true for the larger class of $D$-sets. Moreover we will see that the conclusion of Furstenberg's Central Sets Theorem is true for all sets in this class

Describing the complexity of systems: multi-variable "set complexity" and the information basis of systems biology

Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multi-variable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multi-variable dependency, "differential interaction information." This quantity for two variables reduces to the pairwise "set complexity" previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the "differential interaction information" are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for study of complexity. The properties of "differential interaction information" also suggest new approaches to data analysis. Given a data set of system measurements differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multi-variable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system.Comment: 44 pages, 12 figures; made revisions after peer revie

Simple online learning with consistency oracle

We consider online learning in the model where a learning algorithm can access the class only via the consistency oracle -- an oracle, that, at any moment, can give a function from the class that agrees with all examples seen so far. This model was recently considered by Assos et al. (COLT'23). It is motivated by the fact that standard methods of online learning rely on computing the Littlestone dimension of subclasses, a problem that is computationally intractable. Assos et al. gave an online learning algorithm in this model that makes at most $C^d$ mistakes on classes of Littlestone dimension $d$, for some absolute unspecified constant $C > 0$. We give a novel algorithm that makes at most $O(256^d)$ mistakes. Our proof is significantly simpler and uses only very basic properties of the Littlestone dimension. We also observe that there exists no algorithm in this model that makes at most $2^{d+1}-2$ mistakes. We also observe that our algorithm (as well as the algorithm of Assos et al.) solves an open problem by Hasrati and Ben-David (ALT'23). Namely, it demonstrates that every class of finite Littlestone dimension with recursively enumerable representation admits a computable online learner (that may be undefined on unrealizable samples).Comment: submitted to conferenc

Methylation-sensitive high resolution melting (MS-HRM): a new approach for sensitive and high-throughput assessment of methylation

In this article, we show that high resolution melting analysis (HRM) is a sensitive and specific method for the detection of methylation. Methylated DNA and unmethylated DNA acquire different sequences after bisulphite treatment resulting in PCR products with markedly different melting profiles. We used PCR to amplify both methylated and unmethylated sequences and assessed HRM for the determination of the methylation status of the MGMT promoter region. Reconstruction experiments showed that MGMT methylation could be detected at levels as low as 0.1%. Moreover, MS-HRM allows for estimation of the methylation level by comparing the melting profiles of unknown PCR products to the melting profiles of PCR products derived from standards with a known unmethylated to methylated template ratio. We used MS-HRM for the analysis of eight cell lines of known methylation status and a panel of colorectal cancer specimens. The simplicity and high reproducibility of the MS-HRM protocol makes MS-HRM the method of choice for methylation assessment in many diagnostic and research applications

Nuclear ashes and outflow in the eruptive star Nova Vul 1670

CK Vulpeculae was observed in outburst in 1670-16721, but no counterpart was seen until 1982, when a bipolar nebula was found at its location. Historically, CK Vul has been considered to be a nova (Nova Vul 1670), but a similarity to 'red transients', which are more luminous than classical nova and thought to be the result of stellar collisions, has re-opened the question of CK Vul's status. Red transients cool to resemble late M-type stars, surrounded by circumstellar material rich in molecules and dust. No stellar source has been seen in CK Vul, though a radio continuum source was identified at the expansion centre of the nebula. Here we report CK Vul is surrounded by chemically rich molecular gas with peculiar isotopic ratios, as well as dust. The chemical composition cannot be reconciled with a nova or indeed any other known explosion. In addition, the mass of the surrounding gas is too high for a nova, though the conversion from observations of CO to a total mass is uncertain. We conclude that CK Vul is best explained as the remnant of a merger of two stars.Comment: an older version of an article that appeared in Nature; published in Nature, online version, 23 March 201

On the Relationship between Classical and Deformed Hopf Fibrations

The θ-deformed Hopf fibration S3θ → S2 over the commutative 2-sphere is compared with its classical counterpart. It is shown that there exists a natural isomorphism between the corresponding associated module functors and that the affine spaces of classical and deformed connections are isomorphic. The latter isomorphism is equivariant under an appropriate notion of infinitesimal gauge transformations in these contexts. Gauge transformations and connections on associated modules are studied and are shown to be sensitive to the deformation parameter. A homotopy theoretic explanation for the existence of a close relationship between the classical and deformed Hopf fibrations is proposed

The Relative Role of Bacterial Cell Wall and Capsule in the Induction of Inflammation in Pneumococcal Meningitis

The relative contribution of bacterial components to the induction of inflammation during Streptococcus pneumoniae meningitis is unknown. Several strains of pneumococci with differences in cell surface characteristics (capsule or cell wall) were compared for the effect on the inflammatory response evoked during infection of the cerebrospinal fluid (CSF) in vivo. The presence of bacterial capsular polysaccharide was not necessary for bacterial growth in CSF in vivo but correlated with greater CSF bacterial density. CSF inflammatory changes began to appear when the bacterial concentration exceeded 105 cfu/ml, regardless of the pneumococcal strain. CSF inflammatory changes could be invoked by cisternal instillation of 105−106 cell equivalents of whole, heat-killed unencapsulated strains or their isolated cell walls but not by similar concentrations of heat-killed encapsulated strains or isolated capsular polysaccharide. Hypoglycorrhachia was observed only during inflammation caused by live bacteria. The inflammatory response characteristic of naturally acquired pneumococcal meningitis can be reproduced by challenge with both encapsulated and unencapsulated bacteria. The bacterial cell wall appears to be the most potent pneumococcal surface component in inducing CSF inflammatio

DNA uptake by bacteria and eucaryotic cells

ALEXANDER TOMASZ, The Rockefeller University, New York, New York

A new approach to primer design for the control of PCR bias in methylation studies

Primer design for PCR-based methylation analysis following bisulfite conversion of DNA is considerably more complex than primer design for regular PCR. The choice of the optimal primer set is critical to the performance and correct interpretation of the results. Most methodologies in methylation analysis utilize primers that theoretically amplify methylated and unmethylated templates at the same time. The proportional amplification of all templates is critical but difficult to achieve due to PCR bias favouring the amplification of the unmethylated template. The focus of this brief communication is to point out the important criteria needed for the successful choice of primers that will enable the control of PCR bias in bisulfite based methylation-screening protocols