A study of the separating property in Reed-Solomon codes by bounding the minimum distance

According to their strength, the tracing properties of a code can be categorized as frameproof, separating, IPP and TA. It is known that, if the minimum distance of the code is larger than a certain threshold then the TA property implies the rest. Silverberg et al. ask if there is some kind of tracing capability left when the minimum distance falls below the threshold. Under different assumptions, several papers have given a negative answer to the question. In this paper, further progress is made. We establish values of the minimum distance for which Reed-Solomon codes do not posses the separating property.

Computational aspects of relaxation complexity: possibilities and limitations

The relaxation complexity $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) of the set of integer points X contained in a polyhedron is the smallest number of facets of any polyhedron P such that the integer points in P coincide with X. It is a useful tool to investigate the existence of compact linear descriptions of X. In this article, we derive tight and computable upper bounds on $${{\,\mathrm{rc}\,}}_\mathbb {Q}(X)$$ rc Q ( X ) , a variant of $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) in which the polyhedra P are required to be rational, and we show that $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) can be computed in polynomial time if X is 2-dimensional. Further, we investigate computable lower bounds on $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) with the particular focus on the existence of a finite set $$Y \subseteq \mathbb {Z}^d$$ Y ⊆ Z d such that separating X and $$Y \setminus X$$ Y \ X allows us to deduce $${{\,\mathrm{rc}\,}}(X) \ge k$$ rc ( X ) ≥ k . In particular, we show for some choices of X that no such finite set Y exists to certify the value of $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) , providing a negative answer to a question by Weltge (2015). We also obtain an explicit formula for $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) for specific classes of sets X and present the first practically applicable approach to compute $${{\,\mathrm{rc}\,}}(X)$$ rc ( X ) for sets X that admit a finite certificate.

On the Ger\v{s}gorin disks of distance matrices of graphs

For a simple connected graph $G$, let $D(G)$, $Tr(G)$, $D^{L}(G)=Tr(G)-D(G)$, and $D^{Q}(G)=Tr(G)+D(G)$ be the distance matrix, the diagonal matrix of the vertex transmissions, the distance Laplacian matrix, and the distance signless Laplacian matrix of $G$, respectively. Atik and Panigrahi [2] suggested the study of the problem: Whether all eigenvalues, except the spectral radius, of $ D(G) $ and $ D^{Q}(G) $ lie in the smallest Ger\v{s}gorin disk? In this paper, we provide a negative answer by constructing an infinite family of counterexamples.

No, the Universe Is Not on Our Side

In the 1990 “pale blue dot” photograph that Carl Sagan asked NASA to take, we see the potential of a negative answer to Bernard Lonergan’s question to renew American public life. For Sagan, the isolation of the Earth in the cosmic vastness “underscores our responsibility to deal kindly with each other” and preserve our planet. The conclusion that the universe is not on our side is supported by numerous features of reality: lifeless matter, knowledge limited to the senses, death, decline, the vagaries of history, entropy of the universe, and more. We can accept living in this no. The universe is not hostile, merely neutral. Several thinkers show the way forward, especially John Gray. We can practice Simon Critchley’s faith of the faithless. The instrumental thought of Randy Barnett demonstrates how to construct healthy institutions. Anthony Kronman reminds us that our lives are meaningful only because of our mortality.

ETHICAL AND SOCIOLOGICAL ASSESSMENT OF ATTITUDES TO VACCINATION IN THE YOUTH ENVIRONMENT OF RUSSIA

The prolonged COVID-19 pandemic on the background of a shortage of state resources in the healthcare sphere, caused a wave of pseudoscientific information in the Internet. The youth environment is particularly susceptible to such influence, communication in which has the character of information chaos. To assess the attitude to vaccination in the youth environment of Russia, a sociological study was conducted, N = 480, average age (20.8 ± 1.41). According to the data obtained, 36.71 % of respondents are categorically against personal vaccination. At the same time, only 65.71 % of students who gave a negative answer were able to explain their position. The obtained results demonstrate a tendency to the formation of a socially negative "fashion" among young people – "dissident-vaccines". It is shown that the fundamental difference is that the stigmatization of those who are not vaccinated abroad can be provoked by inequality in access to vaccines, and not a protest manifestation of infodemia, as among young people of Russia. Because of this, the demand for socio-psychological support of vocational education is increasing, where in the conditions of the educational environment, sociological monitoring, moral and psychological correction seems to be the most realistic. In such conditions, the demand for humanitarian education in medical universities is increasing, which allow to focus on ethical norms and moral values of the profession within the educational process.

Periodicities in Cluster Algebras and Cluster Automorphism Groups

We study the relations between two groups related to cluster automorphism groups which are defined by Assem, Schiffler and Shamchenko. We establish the relationships among (strict) direct cluster automorphism groups and those groups consisting of periodicities of labeled seeds and exchange matrices, respectively, in the language of short exact sequences. As an application, we characterize automorphism-finite cluster algebras in the cases of bipartite seeds or finite mutation type. Finally, we study the relation between the group [Formula: see text] for a cluster algebra [Formula: see text] and the group [Formula: see text] for a mutation group [Formula: see text] and a labeled mutation class [Formula: see text], and we give a negative answer via counter-examples to King and Pressland's problem.

Energy Minimisers with Prescribed Jacobian

We consider the class of planar maps with Jacobian prescribed to be a fixed radially symmetric function f and which, moreover, fixes the boundary of a ball; we then study maps which minimise the 2p-Dirichlet energy in this class. We find a quantity $$\lambda [f]$$ λ [ f ] which controls the symmetry, uniqueness and regularity of minimisers: if $$\lambda [f]\le 1$$ λ [ f ] ≤ 1 then minimisers are symmetric and unique; if $$\lambda [f]$$ λ [ f ] is large but finite then there may be uncountably many minimisers, none of which is symmetric, although all of them have optimal regularity; if $$\lambda [f]$$ λ [ f ] is infinite then generically minimisers have lower regularity. In particular, this result gives a negative answer to a question of Hélein (Ann. Inst. H. Poincaré Anal. Non Linéaire 11(3):275–296, 1994). Some of our results also extend to the setting where the ball is replaced by $${\mathbb {R}}^2$$ R 2 and boundary conditions are not prescribed.

A Survey-Based Study of Students’ Expectations vs. Experience of Sustainability Issues in Architectural Education at Wroclaw University of Science and Technology, Poland

Sustainability is currently one of the biggest concerns in the field of architecture and civil engineering. The presented study elaborates on the students’ expectations vs. experience of sustainable and ecological design in their architectural education. Students were surveyed after the interdisciplinary Hybrid Factory Design (HFD) course carried out at the Faculty of Architecture WUST, Poland. Respondents were asked to anonymously fill in a two-part online questionnaire in the last week of the summer semester of the academic year 2020/2021. The questionnaire was composed of 30 compulsory single-choice questions and 8 optional open questions. The single-choice questions were prepared using a five-point Likert scale, ranging from 1 (negative answer) to 5 (positive answer). Additionally, the Expectation Fulfilment Rate (EFR)—an original tool developed by the authors—was used to assess students’ expectations. The conducted survey revealed a significant disproportion between students’ expectations and experience regarding sustainable and ecological design aspects. There are also knowledge gaps in certain areas that should be addressed. Topics related to urban planning, green areas design, renovation and adaptation are not sufficiently represented in the curriculum. Moreover, it is essential to provide students with a broad, cross-disciplinary overview of sustainable architecture to deepen their understanding of different design aspects.

Why Perfect Tests May Not Be Worth Waiting For: Information as a Commodity

Information products provide agents with additional information that can be used to update actions. In many situations, access to such products can be quite limited. For instance, in epidemics, there tends to be a limited supply of medical testing kits, or tests. These tests are information products because their output of a positive or a negative answer informs individuals and authorities on the underlying state and the appropriate course of action. In this paper, using an analytical model, we show how the accuracy of a test in detecting the underlying state affects the demand for the information product differentially across heterogeneous agents. Correspondingly, the test accuracy can serve as a rationing device to ensure that the limited supply of information products is appropriately allocated to the heterogeneous agents. When test availability is low and the social planner is unable to allocate tests in a targeted manner to the agents, we find that moderately good tests can outperform perfect tests in terms of social outcome. This paper was accepted by Charles Corbett, operations management.

Is it possible to determine the sex of the fetus by the Luttge and Mertz'a method? Slotta, Wenger'a and Walter'a (Zentr. F. Gyn., 1926, no. 25)

Numerous studies of Slotta, Wenger'a and Walter'a (Zentr. F. Gyn., 1926, No. 25) give a completely negative answer to this question, and in general these authors consider the underlying idea of L. and M.'s method of the possibility of separating proteins from amino acids 96 alcohol - wrong