Resilience of the rank of random matrices

Let M be an n × m matrix of independent Rademacher (±1) random variables. It is well known that if $n \leq m$ , then M is of full rank with high probability. We show that this property is resilient to adversarial changes to M. More precisely, if $m \ge n + {n^{1 - \varepsilon /6}}$ , then even after changing the sign of (1 – ε)m/2 entries, M is still of full rank with high probability. Note that this is asymptotically best possible as one can easily make any two rows proportional with at most m/2 changes. Moreover, this theorem gives an asymptotic solution to a slightly weakened version of a conjecture made by Van Vu in [17].

Disentangling Item and Testing Effects in Inoculation Research on Online Misinformation: Solomon Revisited

Online misinformation is a pervasive global problem. In response, psychologists have recently explored the theory of psychological inoculation: If people are preemptively exposed to a weakened version of a misinformation technique, they can build up cognitive resistance. This study addresses two unanswered methodological questions about a widely adopted online “fake news” inoculation game, Bad News. First, research in this area has often looked at pre- and post-intervention difference scores for the same items, which may imply that any observed effects are specific to the survey items themselves (item effects). Second, it is possible that using a pretest influences the outcome variable of interest, or that the pretest may interact with the intervention (testing effects). We investigate both item and testing effects in two online studies (total N = 2,159) using the Bad News game. For the item effect, we examine if inoculation effects are still observed when different items are used in the pre- and posttest. To examine the testing effect, we use a Solomon’s Three Group Design. We find that inoculation interventions are somewhat influenced by item effects, and not by testing effects. We show that inoculation interventions are effective at improving people’s ability to spot misinformation techniques and that the Bad News game does not make people more skeptical of real news. We discuss the larger relevance of these findings for evaluating real-world psychological interventions.

Can ChAdOx1, a replication-deficient adenoviral (Ad) vector used to deliver SARS-Cov2 spike protein as a vaccine, recombine with the homologous human Ad to generate a novel Ad+Spike virus?

The development of a vaccine for Covid19 is being expedited [1]. The underlying technology for the vaccines are varied: ‘nucleic acid (DNA and RNA), virus-like particle, peptide, viral vector (replicating and non- replicating), recombinant protein, live attenuated virus and inactivated virus’ [2]. Among these, ChAdOx1, a genetically modified, weakened version of a common cold virus (adenovirus) is now in human clinical trials [3]. The ChAd vector (Chimpanzee adenovirus) was introduced in 2012 Chimpanzee adenovirus Y25 [4]. A large proportion of human adults possess significant titres of neutralising antibodies to human Adv, hence the requirement for a different adenovirus. The deletion of a single transcriptional unit, E1, ensures these viruses cant replicate. Other genes like the E3 region may also be deleted. Now, in the Covid19 vaccine ChAdOx1, the spike protein gene from MERS-CoV strain Camel/Qatar/2/2014 ‘was inserted into the E1 locus of a genomic clone of ChAdOx1 using site-specific recombination’ [5].One of the theories about the genesis of SARS-Cov2 is recombination with coronaviruses from pan- golins [6]. Whether or not it happened in SARS-Cov2, there is no denying that such recombinations do happen.How do we know that the spike protein wont be inserted into a human adenovirus using recombination?Human adenovirus shares 95% homology to ChAd. The spike protein may be inserted after the E1 protein in a viable human virus. What will happen after that to the virus is anyone’s guess. Note, that there is precedence for such recombinant adenoviruses - using ‘ping-pong” zoonosis and anthroponosis’, where the genome of a promiscuous pathogen is ‘embedded with evidence of unprecedented multiple, multidirectional, stable, and reciprocal cross-species infections of hosts from three species (human, chimpanzee, and bonobo)’ [7].Another critique - co-stimulation in host cellsA spike protein from SARS-Cov2, which is supposed to bind to ACE2 and CD147 [8], has been inserted in an adenovirus. The adenovirus has its own host-cell receptor preferences [9] - what will be the consequences of co-stimulation in those cells in which both these receptors are expressed?

FACTORS OF CARMICHAEL NUMBERS AND AN EVEN WEAKER -TUPLES CONJECTURE

One of the open questions in the study of Carmichael numbers is whether, for a given $R\geq 3$ , there exist infinitely many Carmichael numbers with exactly $R$ prime factors. Chernick [‘On Fermat’s simple theorem’, Bull. Amer. Math. Soc. 45 (1935), 269–274] proved that Dickson’s $k$ -tuple conjecture would imply a positive result for all such $R$ . Wright [‘Factors of Carmichael numbers and a weak $k$ -tuples conjecture’, J. Aust. Math. Soc. 100(3) (2016), 421–429] showed that a weakened version of Dickson’s conjecture would imply that there are an infinitude of $R$ for which there are infinitely many such Carmichael numbers. In this paper, we improve on our 2016 result by weakening the required conjecture even further.

A Modular André–Oort Statement with Derivatives

In unpublished notes, Pila discussed some theory surrounding the modular function j and its derivatives. A focal point of these notes was the statement of two conjectures regarding j, j′ and j″: a Zilber–Pink-type statement incorporating j, j′ and j″, which was an extension of an apparently weaker conjecture of André–Oort type. In this paper, I first cover some background regarding j, j′ and j″, mostly covering the work already done by Pila. Then I use a seemingly novel adaptation of the o-minimal Pila–Zannier strategy to prove a weakened version of Pila's ‘Modular André–Oort with Derivatives’ conjecture. Under the assumption of a certain number-theoretic conjecture, the central theorem of the paper implies Pila's conjecture in full generality, as well as a more precise statement along the same lines.

State sum invariants of three manifolds from spherical multi-fusion categories

We define a family of quantum invariants of closed oriented [Formula: see text]-manifolds using spherical multi-fusion categories (SMFCs). The state sum nature of this invariant leads directly to [Formula: see text]-dimensional topological quantum field theories ([Formula: see text]s), which generalize the Turaev–Viro–Barrett–Westbury ([Formula: see text]) [Formula: see text]s from spherical fusion categories. The invariant is given as a state sum over labeled triangulations, which is mostly parallel to, but richer than the [Formula: see text] approach in that here the labels live not only on [Formula: see text]-simplices but also on [Formula: see text]-simplices. It is shown that a multi-fusion category in general cannot be a spherical fusion category in the usual sense. Thus, we introduce the concept of a SMFC by imposing a weakened version of sphericity. Besides containing the [Formula: see text] theory, our construction also includes the recent higher gauge theory [Formula: see text]-[Formula: see text]s given by Kapustin and Thorngren, which was not known to have a categorical origin before.

Degree bounds on homology and a conjecture of Derksen

Harm Derksen made a conjecture concerning degree bounds for the syzygies of rings of polynomial invariants in the non-modular case [Degree bounds for syzygies of invariants, Adv. Math. 185 (2004), 207–214]. We provide counterexamples to this conjecture, but also prove a slightly weakened version. We also prove some general results that give degree bounds on the homology of complexes and of $\text{Tor}\,$ groups.

Fighting Nature: An Analysis and Critique of Breed-Specific Flourishing Arguments for Dog Fights

Social science literature on dog fighting illustrates an important element in the discourse of dog fighters, namely patriarchy. However, it has not addressed another common element, namely flourishing. According to this element of that discourse, some dog breeds are born to fight, and therefore dog fighters are helping them achieve their best lives. This argument is explicitly made by dog fighters, and it is inadvertently supported by those trying to give other dogs breed-specific flourishing, and those who advocate for breed-specific legislation. This poses a problem for advocates of using flourishing to understand animal welfare, particularly if they use kinds (like species and breed) to determine what counts as a flourishing life for a particular nonhuman animal. I argue that we can keep a slightly weakened version of breed-specific flourishing as a starting place for understanding individual dogs without endorsing sport fighting or breed-specific legislation for “vicious” breeds of dogs.

Ample thoughts

Non-n-ampleness as denned by Pillay [20] and Evans [5] is preserved under analysability. Generalizing this to a more general notion of Σ-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis [4] for types of finite SU-rank. This is then applied to the special case of groups.