Ramanujan graphs in cryptography

In this paper we study the security of a proposal for Post-Quantum Cryptography from both a number theoretic and cryptographic perspective. Charles-Goren-Lauter in 2006 [CGL06] proposed two hash functions based on the hardness of finding paths in Ramanujan graphs. One is based on Lubotzky-Phillips-Sarnak (LPS) graphs and the other one is based on Supersingular Isogeny Graphs. A 2008 paper by Petit-Lauter-Quisquater breaks the hash function based on LPS graphs. On the Supersingular Isogeny Graphs proposal, recent work has continued to build cryptographic applications on the hardness of finding isogenies between supersingular elliptic curves. A 2011 paper by De Feo-Jao-Pl\^{u}t proposed a cryptographic system based on Supersingular Isogeny Diffie-Hellman as well as a set of five hard problems. In this paper we show that the security of the SIDH proposal relies on the hardness of the SIG path-finding problem introduced in [CGL06]. In addition, similarities between the number theoretic ingredients in the LPS and Pizer constructions suggest that the hardness of the path-finding problem in the two graphs may be linked. By viewing both graphs from a number theoretic perspective, we identify the similarities and differences between the Pizer and LPS graphs.Comment: 33 page

Correction factors for Kac-Moody groups and tt-deformed root multiplicities

We study a correction factor for Kac-Moody root systems which arises in the theory of $p$-adic Kac-Moody groups. In affine type, this factor is known, and its explicit computation is the content of the Macdonald constant term conjecture. The data of the correction factor can be encoded as a collection of polynomials $m_\lambda \in \mathbb{Z}[t]$ indexed by positive imaginary roots $\lambda$. At $t=0$ these polynomials evaluate to the root multiplicities, so we consider $m_\lambda$ to be a $t$-deformation of $\mathrm{mult} (\lambda)$. We generalize the Peterson algorithm and the Berman-Moody formula for root multiplicities to compute $m_\lambda$. As a consequence we deduce fundamental properties of $m_\lambda$.Comment: 17 page

Arithmetic geometry of character varieties with regular monodromy

We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the character variety are smooth and equidimensional. Next, we count points on a family of smooth character varieties; namely, those involving regular semisimple and regular unipotent monodromy. In particular, we show that these varieties are polynomial count and obtain an explicit expression for their $E$-polynomials. Finally, by analysing the $E$-polynomial, we determine certain topological properties of these varieties such as the Euler characteristic and the number of connected components.Comment: Paper was re-written for v2, making it much easier to follow. A missing assumption on $q$ in the main theorem was adde

“Blood Antiquities” of Africa: A Link between Illicit Trafficking of Cultural Property and Terrorism-Financing?

In the light of recent years’ armed conflicts and the growing level of terrorist activity globally, the link between illicit trafficking of cultural property and terrorism constitutes a growing concern for war-torn regions as well as for the international community as a whole. Identified as a possible form of terrorism-financing in recent years, the illegal trade of artefacts contributes to the fuelling of the spiral of violence and by this, to the undermining of the identity of the targeted populations. Due to the effects of the Arab Spring swiping through several African countries resulting in a still-existing destabilisation, power vacuum and the spread of different terrorist groups, these countries are serving an especially timeous example from this point of view. By presenting some examples from North Africa and the Sahel region, the paper aims to give an initial insight into the issue as an increasingly important international security challenge

Strict and non-strict negative concord in Hungarian: A unified analysis

Surányi (2006) observed that Hungarian has a hybrid (strict + non-strict) negative concord system. This paper proposes a uniform analysis of that system within the general framework of Zeijlstra (2004, 2008) and, especially, Chierchia (2013), with the following new ingredients. Sentential negation NEM is the same full negation in the presence of both strict and non-strict concord items. Preverbal SENKI `n-one’ type negative concord items occupy the specifier position of either NEM `not' or SEM `nor'. The latter, SEM spells out IS `too, even’ in the immediate scope of negation; it is a focus-sensitive head on the clausal spine. SEM can be seen as an overt counterpart of the phonetically null head that Chierchia dubs NEG; it is capable of invoking an abstract (disembodied) negation at the edge of its projection

Edaravone protects against methylglyoxal-induced barrier damage in human brain endothelial cells

BACKGROUND: Elevated level of reactive carbonyl species, such as methylglyoxal, triggers carbonyl stress and activates a series of inflammatory responses leading to accelerated vascular damage. Edaravone is the active substance of a Japanese medicine, which aids neurological recovery following acute brain ischemia and subsequent cerebral infarction. Our aim was to test whether edaravone can exert a protective effect on the barrier properties of human brain endothelial cells (hCMEC/D3 cell line) treated with methylglyoxal. METHODOLOGY: Cell viability was monitored in real-time by impedance-based cell electronic sensing. The barrier function of the monolayer was characterized by measurement of resistance and flux of permeability markers, and visualized by immunohistochemistry for claudin-5 and β-catenin. Cell morphology was also examined by holographic phase imaging. PRINCIPAL FINDINGS: Methylglyoxal exerted a time- and dose-dependent toxicity on cultured human brain endothelial cells: a concentration of 600 µM resulted in about 50% toxicity, significantly reduced the integrity and increased the permeability of the barrier. The cell morphology also changed dramatically: the area of cells decreased, their optical height significantly increased. Edaravone (3 mM) provided a complete protection against the toxic effect of methylglyoxal. Co-administration of edaravone restored cell viability, barrier integrity and functions of brain endothelial cells. Similar protection was obtained by the well-known antiglycating molecule, aminoguanidine, our reference compound. CONCLUSION: These results indicate for the first time that edaravone is protective in carbonyl stress induced barrier damage. Our data may contribute to the development of compounds to treat brain endothelial dysfunction in carbonyl stress related diseases

Comparison of humoral and cellular immune responses in hematologic diseases following completed vaccination protocol with BBIBP-CorV, or AZD1222, or BNT162b2 vaccines against SARS-CoV-2

BackgroundVaccination has proven the potential to control the COVID-19 pandemic worldwide. Although recent evidence suggests a poor humoral response against SARS-CoV-2 in vaccinated hematological disease (HD) patients, data on vaccination in these patients is limited with the comparison of mRNA-based, vector-based or inactivated virus-based vaccines.MethodsForty-nine HD patients and 46 healthy controls (HCs) were enrolled who received two-doses complete vaccination with BNT162b2, or AZD1222, or BBIBP-CorV, respectively. The antibodies reactive to the receptor binding domain of spike protein of SARS-CoV-2 were assayed by Siemens ADVIA Centaur assay. The reactive cellular immunity was assayed by flow cytometry. The PBMCs were reactivated with SARS-CoV-2 antigens and the production of activation-induced markers (TNF-α, IFN-γ, CD40L) was measured in CD4+ or CD8+ T-cells ex vivo.ResultsThe anti-RBD IgG level was the highest upon BNT162b2 vaccination in HDs (1264 BAU/mL) vs. HCs (1325 BAU/mL) among the studied groups. The BBIBP-CorV vaccination in HDs (339.8 BAU/mL ***p < 0.001) and AZD1222 in HDs (669.9 BAU/mL *p < 0.05) resulted in weaker antibody response vs. BNT162b2 in HCs. The response rate of IgG production of HC vs. HD patients above the diagnostic cut-off value was 100% vs. 72% for the mRNA-based BNT162b2 vaccine; 93% vs. 56% for the vector-based AZD1222, or 69% vs. 33% for the inactivated vaccine BBIBP-CorV, respectively. Cases that underwent the anti-CD20 therapy resulted in significantly weaker (**p < 0.01) anti-RBD IgG level (302 BAU/mL) than without CD20 blocking in the HD group (928 BAU/mL). The response rates of CD4+ TNF-α+, CD4+ IFN-γ+, or CD4+ CD40L+ cases were lower in HDs vs. HCs in all vaccine groups. However, the BBIBP-CorV vaccine resulted the highest CD4+ TNF-α and CD4+ IFN-γ+ T-cell mediated immunity in the HD group.ConclusionWe have demonstrated a significant weaker overall response to vaccines in the immunologically impaired HD population vs. HCs regardless of vaccine type. Although, the humoral immune activity against SARS-CoV-2 can be highly evoked by mRNA-based BNT162b2 vaccination compared to vector-based AZD1222 vaccine, or inactivated virus vaccine BBIBP-CorV, whereas the CD4+ T-cell mediated cellular activity was highest in HDs vaccinated with BBIBP-CorV