Alfréd Rényi Institute of Mathematics

The absence of an immediately deployable, broad-spectrum antiviral remains a critical vulnerability in global pandemic preparedness. Host-directed agents that activate innate immunity offer a pathogen-agnostic strategy, yet no such therapy is currently stockpiled or authorized for emergency use. Infectious Bursal Disease Virus (IBDV)-a non-replicating avian dsRNA vaccine virus with a 60-year safety record in poultry-induces robust interferon responses in mammals and has been administered orally in marmosets and more than 50 human patients with hepatitis A, B, C, SARS-CoV-2, and herpes zoster infections. These observations include a randomized phase II trial in 84 acute HBV/HCV patients. Although the evidence base is limited, the consistency of clinical responses and absence of serious safety signals justify renewed scientific examination. This review synthesizes the mechanistic rationale, comparative advantages over synthetic Pattern Recognition Receptor (PRR) agonists, clinical observations, One Health implications, and regulatory precedents relevant to evaluating IBDV as a temporary, compassionate-use antiviral during pandemics while the reverse-engineered human candidate (IBDV-R903/78) progresses through formal development. The goal is not to endorse clinical deployment, but to initiate a rigorous, multidisciplinary debate on whether an established veterinary dsRNA vaccine virus could serve as an off-the-shelf host-directed live viral adjuvant therapy in future public health emergencies.

Abstract A classical theorem of Macbeath states that for any integers , , ‐dimensional Euclidean balls are hardest to approximate, in terms of volume difference, by inscribed convex polytopes with vertices. In this paper, we investigate normed variants of this problem: we intend to find the extremal values of the Busemann volume, Holmes–Thompson volume, Gromov's mass, and Gromov's of a largest volume convex polytope with vertices, inscribed in the unit ball of a ‐dimensional normed space.

It is possible to have a packing by translates of a cube that is maximal (i.e. no other cube can be added without overlapping) but does not form a tiling. In the long running analogy of packing and tiling to orthogonality and completeness of exponentials on a domain, we pursue the question whether one can have maximal orthogonal sets of exponentials for a cube without them being complete. We prove that this is not possible in dimensions 1 and 2, but is possible in dimensions 3 and higher. We provide several examples of such maximal incomplete sets of exponentials, differing in size, and we raise relevant questions. We also show that even in dimension 1 there are sets which are spectral (i.e. have a complete set of orthogonal exponentials) and yet they also possess maximal incomplete sets of orthogonal exponentials.

Abstract We introduce the concept of quotient-convergence for sequences of submodular set functions, providing, among others, a new framework for the study of convergence of matroids through their rank functions. Extending the limit theory of bounded degree graphs, which analyzes graph sequences via neighborhood sampling, we address the challenge posed by the absence of a neighborhood concept in matroids. We show that any bounded set function can be approximated by a sequence of finite set functions that quotient-converges to it. In addition, we explicitly construct such sequences for increasing, submodular, and upper continuous set functions, and prove the completeness of the space under quotient-convergence.

The transition from high school to university-level mathematics is often accompanied by significant challenges. During the COVID-19 pandemic, these difficulties were further exacerbated by the abrupt shift to online learning. In response, educators increasingly turned to gamification—“a process of enhancing a service with affordances for gameful experiences in order to support users’ overall value creation”—as a strategy to address the limitations of remote instruction. In this study, we designed a gamified environment for a first-year Number Theory course. The system was constructed using targeted game elements such as leaderboards, optional challenge exams, and recognition for elegant solutions. These features were then integrated into a comprehensive point-based assessment system, which accounted for weekly quizzes and active participation. Following a quasi-experimental design, this study compared two groups of pre-service mathematics teachers: the class of 2017 (N = 62), which received traditional in-person instruction (control group), and the class of 2020 (N = 61), which participated in an online, gamified version of the course (experimental group). Both groups were taught by the same lecturer, using identical content, concepts, and similar tasks throughout the course. Academic performance was measured using midterm exam results. While no significant difference emerged on the first midterm in week 6 (their average percentages were 50% and 51%), the experimental group significantly outperformed the control group on the second midterm at the end of the term (their average percentages were 65% and 49%). These results suggest that a thoughtfully designed, gamified approach can enhance learning outcomes in an online mathematics course.

In the affine space \(\mathbb{F}_q^n\) over the finite field of order \(q\), a point set \(S\) is said to be \((d,k,r)\)-evasive if the intersection between \(S\) and any variety, of dimension \(k\) and degree at most \(d\), has cardinality less than \(r\). As \(q\) tends to infinity, the size of a \((d,k,r)\)-evasive set in \(\mathbb{F}_q^n\) is at most \(O(q^{n-k})\) by a simple averaging argument. We exhibit the existence of such evasive sets of sizes at least \(\Omega(q^{n-k})\) for much smaller values of \(r\) than previously known constructions, and establish an enumerative upper bound \(2^{O(q^{n-k})}\) for the total number of such evasive sets. The existence result is based on our study of twisted varieties. In the projective space \(\mathbb{P}^n\) over an algebraically closed field, a variety \(V\) is said to be \(d\)-twisted if the intersection between \(V\) and any variety of dimension \(n-\dim(V)\) and degree at most \(d\) has dimension zero. We prove an upper bound on the smallest possible degree of twisted varieties which is best possible in a mild sense. The enumeration result includes a new technique for the container method which we believe is of independent interest. To illustrate the potential of this technique, we give a simpler proof of a result by Chen–Liu–Nie–Zeng that characterizes the maximum size of a collinear-triple-free subset in a random sampling of \(\mathbb{F}_q^2\) up to polylogarithmic factors.