Related papers: Access Structures Determined by Uniform Polymatroi…
In this paper, we establish a one-to-one correspondence between the set of biclosed sets in an irreducible root system of type $A_n$ and the set of quasitrivial semigroup structures on a set with $n+1$ elements. Building on this…
A subset $S$ of $\mathbb R^d$ has the Borsuk property if it can be decomposed into at most $d+1$ parts of diameter smaller than $S$. This is an important geometric property, inspired by a conjecture of Borsuk from the 1930s, which has…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
Abstract separation systems are a new unifying framework in which separations of graph, matroids and other combinatorial structures can be expressed and studied. We characterize the abstract separation systems that have representations as…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
Secret sharing is a method of dividing a secret among n par- ticipants and allows only qualified subset to reconstruct the secret and hence provides better reliability and availability of secret data.In the generalized secret sharing…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences…
Our recent paper [Grauwin et al. Sci. Rep. 7 (2017)] demonstrates that community and hierarchical structure of the networks of human interactions largely determines the least and should be taken into account while modeling them. In the…
Many cryptographic protocols are intended to coordinate state changes among principals. Exchange protocols coordinate delivery of new values to the participants, e.g. additions to the set of values they possess. An exchange protocol is fair…
Multipartite entanglement is one of the crucial resources in quantum information processing tasks such as quantum metrology, quantum computing and quantum communications. It is essential to verify not only the multipartite entanglement, but…
We consider three forms of composition of matroids, each of which extends the category of bimatroids to a rigid monoidal category. Many well-known constructions are functorial or defined by morphisms in these categories. Motivating examples…
We propose a secure multi-party computation (MPC) protocol that constructs a secret-shared decision tree for a given secret-shared dataset. The previous MPC-based decision tree training protocol (Abspoel et al. 2021) requires $O(2^hmn\log…
The problem of optimal resource allocation is studied for ergodic fading orthogonal multiaccess relay channels (MARCs) in which the users (sources) communicate with a destination with the aid of a half-duplex relay that transmits on a…
This work aims to show the applicability, and how, of privacy by design approach to biometric systems and the benefit of using formal methods to this end. Starting from a general framework that has been introduced at STM in 2014, that…
Rough sets are efficient for data pre-processing in data mining. As a generalization of the linear independence in vector spaces, matroids provide well-established platforms for greedy algorithms. In this paper, we apply rough sets to…
We study social welfare of learning outcomes in mechanisms with admission. In our repeated game there are $n$ bidders and $m$ mechanisms, and in each round each mechanism is available for each bidder only with a certain probability. Our…
A theory of single-element extensions of integer polymatroids analogous to that of matroids is developed. We present an algorithm to generate a catalog of $2$-polymatroids, up to isomorphism. When we implemented this algorithm on a…
We design an FPRAS to count the number of bases of any matroid given by an independent set oracle, and to estimate the partition function of the random cluster model of any matroid in the regime where $0<q<1$. Consequently, we can sample…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…