Through the lens of social constructionism: the development of innovative anti-corruption policies and practices in Bulgaria, Greece and Romania, 2000–2015

The past decade has witnessed two distinct yet interconnected developments in the understanding, policy and practice of corruption studies. On the one hand, corruption has progressively been constructed as a major threat to economic and social development through the use of deceivingly simplistic Western-centric definitions,1 awareness campaigns and international perception-indexes that create the illusion of measuring real levels of corruption. Such developments have recently been criticized by academic observers and activists alike for presenting corruption as a country-specific issue, closely linked to the public sector. On the other hand, and perhaps counterintuitively, anti-corruption efforts have been decontextualized, focusing on generic fixes that typically involve the public sector. This one-size-fits-all approach has not produced impressive results, and has come under attack for ignoring the historical context and function of contemporary states

Energy bounds for codes and designs in Hamming spaces

We obtain universal bounds on the energy of codes and for designs in Hamming spaces. Our bounds hold for a large class of potential functions, allow unified treatment, and can be viewed as a generalization of the Levenshtein bounds for maximal codes.Comment: 25 page

Next levels universal bounds for spherical codes: the Levenshtein framework lifted

We introduce a framework based on the Delsarte-Yudin linear programming approach for improving some universal lower bounds for the minimum energy of spherical codes of prescribed dimension and cardinality, and universal upper bounds on the maximal cardinality of spherical codes of prescribed dimension and minimum separation. Our results can be considered as next level universal bounds as they have the same general nature and imply, as the first level bounds do, necessary and sufficient conditions for their local and global optimality. We explain in detail our approach for deriving second level bounds. While there are numerous cases for which our method applies, we will emphasize the model examples of $24$ points ($24$-cell) and $120$ points ($600$-cell) on $\mathbb{S}^3$. In particular, we provide a new proof that the $600$-cell is universally optimal, and furthermore, we completely characterize the optimal linear programing polynomials of degree at most $17$ by finding two new polynomials, which together with the Cohn-Kumar's polynomial form the vertices of the convex hull that consists of all optimal polynomials. Our framework also provides a conceptual explanation of why polynomials of degree $17$ are needed to handle the $600$-cell via linear programming.Comment: 30 pages, 4 figures, 5 tables, submitte

On polarization of spherical codes and designs

In this article we investigate the $N$-point min-max and the max-min polarization problems on the sphere for a large class of potentials in $\mathbb{R}^n$. We derive universal lower and upper bounds on the polarization of spherical designs of fixed dimension, strength, and cardinality. The bounds are universal in the sense that they are a convex combination of potential function evaluations with nodes and weights independent of the class of potentials. As a consequence of our lower bounds, we obtain the Fazekas-Levenshtein bounds on the covering radius of spherical designs. Utilizing the existence of spherical designs, our polarization bounds are extended to general configurations. As examples we completely solve the min-max polarization problem for $120$ points on $\mathbb{S}^3$ and show that the $600$-cell is universally optimal for that problem. We also provide alternative methods for solving the max-min polarization problem when the number of points $N$ does not exceed the dimension $n$ and when $N=n+1$. We further show that the cross-polytope has the best max-min polarization constant among all spherical $2$-designs of $N=2n$ points for $n=2,3,4$; for $n\geq 5$, this statement is conditional on a well-known conjecture that the cross-polytope has the best covering radius. This max-min optimality is also established for all so-called centered codes

Computing Distance Distributions of Ternary Orthogonal Arrays

Orthogonal Arrays (OA) play important roles in statistics (used in designing experiments), computer science and cryptography. The most important problems are those about their existence and classification of non-isomorphic classes of OA with given parameters. The solving of these problems requires possible Hamming distance distributions of studied orthogonal array to be determined. In this paper we propose a method for computing of distance distributions of OA with given parameters. Comparing computed possible distance distributions of the considered OA with ones of its derivative OAs we proved some nonexistence results and found some restrictions over structure of the studied OA.Grant KP-06N32/1-2019 of the Bulgarian National Science Fund; Contract 80-10-151/24.04.2020 of the Science Foundation of Sofia University; Grant KP-06-N32/2-2019 of the Bulgarian National Science Fund