Independent sets of a given size and structure in the hypercube

We determine the asymptotics of the number of independent sets of size $\lfloor \beta 2^{d-1} \rfloor$ in the discrete hypercube $Q_d = \{0,1\}^d$ for any fixed $\beta \in (0,1)$ as $d \to \infty$ , extending a result of Galvin for $\beta \in (1-1/\sqrt{2},1)$ . Moreover, we prove a multivariate local central limit theorem for structural features of independent sets in $Q_d$ drawn according to the hard-core model at any fixed fugacity $\lambda>0$ . In proving these results we develop several general tools for performing combinatorial enumeration using polymer models and the cluster expansion from statistical physics along with local central limit theorems.

Revisiting prophylaxis of homeopathic interventions in COVID 19

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) caused by novel beta-coronavirus has emerged as a cause of coronavirus pandemic (COVID-19) declared by Public Health Emergency of International Concern (PHEIC). Korean oriental medicine, Traditional Chinese Medicine (TCM), and Indian systems of medicine known as AYUSH (Ayurveda, Yoga and Naturopathy, Unani, Siddha and Sowa-Rigpa and Homeopathy) had implemented various prophylactic measures and interim treatment guidelines in prevention and treatment for COVID -19 cases. However, even though different approaches were implemented to break the epidemic chain, we have not reached herd effect or herd immunity in the Indian population. Therefore, in this ongoing COVID-19 pandemic, a specific study on immune markers of IL-6 (Interleukin-6), D-Dimer, Ferritine, CRP (C-reactive protein) with SARS CoV-2 specific IgG & IgM antibodies need to be investigated for generating hard-core evidence for homeoprophylaxis in terms of immunity response. Therefore, there seems to be a need to revisit the program of homeoprophylaxis in the COVID -19 pandemic.

A Normative Model of Politically Neutral Expertise

Increasing interaction between science and politics requires analysis of the risks of science politicization. The author considers the threat of political control over the expertise and proposes a normative model which allows to avoid this threat. The author argues that the protection of the “hard core” of scientific rationality of expert’s activity is possible if the role of scientists is limited to the “technical” stage of the expertise (aggregation of scientific consensus on the problem). At this stage, the experts should make risks of the proposed strategies visible for public (the author calls this “risks externalization”). In turn, a decision on the compliance of the proposed strategies with the political interests of society should be made at the stage of open discussion. The author claims that separation of these two levels of expertise has the following advantages: (1) allows one to minimize moral and political pressure on experts; (2) makes it possible to involve all parties in the discussion, thereby neutralizing “privatization” of the public sphere; (3) allows one to aggregate distributed knowledge; (4) provides an opportunity for the distribution of responsibility among wider range of participants, thereby maintaining the democratic spirit in the community. The author criticizes the idea of “expert decisionism” and claims that it should be considered as an exceptional mode of expertise in extraordinary situation.

Yes, science dial is extremely costly, but...

Those who believe in the simplistic trust model between politics and science unintentionally (or intentionally) omit the fact that there exists something called cultural value systems and norms, which govern the formation, growth and demise of a group. These elements are so critical that by setting them aside, we risk entering total disagreements whenever difficult problems arise. One such serious problem is the climate crisis and the need for building the eleventh cultural value as proposed by Vuong [7]. And this value will complement the progressive value system suggested by Harrison [8]. It is safe to say that besides hard-core sciences, resolving global problems posing existential threats to humankind will certainly require us to deploy our best weapons, and many must come from the social sciences and humanities [9]. Therefore, the future solution to global change problems will have to show us its social heart.

Induced surface and curvature tension equation of state for hadron resonance gas in finite volumes and its relation to morphological thermodynamics

Here, we develop an original approach to investigate the grand canonical partition function of the multicomponent mixtures of Boltzmann particles with hard-core interaction in finite and even small systems of the volumes above 20 fm3. The derived expressions of the induced surface tension equation of state (EoS) are analyzed in detail. It is shown that the metastable states, which can emerge in the finite systems with realistic interaction, appear at very high pressures at which the hadron resonance gas, most probably, is not applicable at all. It is shown how and under what conditions the obtained results for finite systems can be generalized to include into a formalism the equation for curvature tension. The applicability range of the obtained equations of induced surface and curvature tensions for finite systems is discussed and their close relations to the equations of the morphological thermodynamics are established. The hadron resonance gas model on the basis of the obtained advanced EoS is worked out. Also, this model is applied to analyze the chemical freeze-out of hadrons and light nuclei with the number of (anti-) baryons not exceeding 4. Their multiplicities were measured by the ALICE Collaboration in the central lead–lead collisions at the center-of-mass energy [Formula: see text] TeV.

How Well Does Evolution Explain Endogenous Retroviruses?—A Lakatosian Assessment

One of the most sophisticated philosophies of science is the methodology of scientific research programmes (MSRP), developed by Imre Lakatos. According to MSRP, scientists are working within so-called research programmes, consisting of a hard core of fixed convictions and a flexible protective belt of auxiliary hypotheses. Anomalies are accommodated by changes to the protective belt that do not affect the hard core. Under MSRP, research programmes are appraised as ‘progressive’ if they successfully predict novel facts but are judged as ‘degenerative’ if they merely offer ad hoc solutions to anomalies. This paper applies these criteria to the evolutionary research programme as it has performed during half a century of ERV research. It describes the early history of the field and the emergence of the endogenization-amplification theory on the origins of retroviral-like sequences. It then discusses various predictions and postdictions that were generated by the programme, regarding orthologous ERVs in different species, the presence of target site duplications and the divergence of long terminal repeats, and appraises how the programme has dealt with data that did not conform to initial expectations. It is concluded that the evolutionary research programme has been progressive with regard to the issues here examined.

Fennougristiikan historiaa Virittäjän valossa

Artikkeli tarkastelee yhtäältä 125 vuotta täyttävän aikakauslehti Virittäjän historiaa fennougristiikan valossa, toisaalta fennougristiikan historiaa Virittäjän valossa. Päähuomio on erityisesti suomen etäsukukielten tutkimuksessa. Virittäjässäkin fennougristiikkaa ovat tyypillisimmin edustaneet konkreettiset pyrkimykset suomen ja sen sukukielten menneisyyden valaisemiseksi: keskiössä ovat olleet toisiinsa kietoutuneet etymologia ja äännehistoria sekä niiden kehyksiksi hahmotellut kantakielet eri vaiheineen ja kontaktikielineen. Tämän fennougristiikan kovan ytimen lisäksi Virittäjässä ovat kuitenkin aina olleet näkyvissä myös tieteenalan suuremmat kehykset: yhtäältä pohdinnat siitä, miksi ja miten tällaista tutkimusta harjoitetaan, toisaalta halu kertoa fennougristisen tutkimuksen tuloksista myös suurelle yleisölle. Erityisesti Suomi ja täällä etenkin Virittäjä ovat ympäristöjä, joissa suomalais-ugrilaisten kielten tutkijat ovat kerta toisensa jälkeen eksplisiittisesti pohtineet olemassaolonsa tarkoitusta. Vaikka ala mielletään usein kielihistorian tutkimukseksi, fennougristit ovat aina harjoittaneet myös synkronista kielentutkimusta; myös suomen sukukielten uhan­alaisuuteen ja vähemmistökielten puhujien oikeuksiin on kiinnitetty huomiota jo 1800-luvulta lähtien. Artikkeli keskittyy lähinnä Virittäjän ensimmäiselle vuosisadalle, mutta 2020-luvulle tultaessa fennougristiikka ja sen ilmenemismuodot Virittäjässä ovat muuttuneet lehden yleisilmeeseen verrattuna suhteellisen vähän. On the history of Uralic linguistics in Virittäjä The article provides an account of Virittäjä, the major journal of Finnish linguistics established in 1897, and its relation to the study of Uralic languages during the first 125 years of the journal’s history. At its most typical, the study of Uralic languages has been a branch of historical-comparative linguistics aiming to pursue the distant past of Finnish and other Uralic languages: etymology, historical phonology, questions of proto-languages and their chronology and geography as well as language contacts. Beyond this hard core of Uralic linguistics, Virittäjä has continuously provided a forum for discussing the larger frameworks of the discipline: questions of why and how Uralic linguistics is conducted in the first place. Virittäjä has also provided a forum for Uralicists to communicate the results of their research to scholars of Finnish and the wider general public. Moreover, Finland in general and Virittäjä in particular have traditionally been places where Uralicists have pondered and discussed the purpose of their own existence. In addition to historical linguistics, Uralicists have also engaged in synchronic linguistics, and from as early as the 19th century they have also paid attention to language endangerment and the linguistic rights of minorities. This article focuses mainly on the first century of Virittäjä’s history, though by the 2020s Uralistics and the manifestations of the discipline in the pages of Virittäjä have remained largely unchanged.