Almost surely, the difference between the randomness deficiencies of two infinite sequences will be unbounded with respect to repeated iterations of the shift operator.
The Independence Postulate (IP) is a finitary Church-Turing Thesis, saying mathematical sequences are independent from physical ones. IP implies the existence of anomalies.
In 2011, Harrigan and Healy published a polynomial-time algorithm for one-sided crossing minimization for trees. We point out a counterexample to that algorithm, and show that one-sided crossing minimization is NP-hard for trees.
The Independence Postulate (IP) is a finitary Church-Turing Thesis, saying mathematical sequences are independent from physical ones. Modelling observations as infinite sequences of real numbers, IP implies the existence of anomalies.
As a Small Island Developing State, Seychelles is disproportionately affected by climate change, and enhancing her adaptive capacity is a national priority. Identifying and integrating local capacity needs into policy measures can improve multilevel governance and the effective implementation of National Adaptation Plans (NAPs), given that local governments have contextual knowledge about their territories and the climate change challenges affecting them. Based on the Capital Approach Framework (CAF), this study carries out an analysis of local governance capacity needs for implementing climate change adaptation in Seychelles. Data were collected using two methods: (i) questionnaire-led interviews among twenty-four district administrators (DAs), and (ii) an interactive workshop involving thirty-one participants, of which twenty-six were DAs and five were members of the National Climate Change Committee. The CAF was measured in two ways: (i) through descriptive statistics such as frequencies based on interview data, and (ii) through the ranking of types of capital to assess their weightings across four categories using a consensus approach during the participatory workshop. The findings of this study indicate significant political, financial, and human resource capacity gaps, which collectively hinder local adaptation. The critical shortcomings identified include the low participation in national-level decision-making processes, the inability to access external funding sources, and the lack of technical know-how. Through a participatory approach involving the local government representatives and the National Climate Change Committee, ten recommendations for policy measures that can enhance the effectiveness of local governance in climate change adaptation were co-developed. Seven of these recommendations partly address issues related to political capital. These recommendations highlight that a siloed approach cannot effectively address the impacts of climate change. For example, one of the recommendations stated that land-use planning should be guided by location-specific vulnerabilities, as these differ across districts.
In the past a few years, many interesting inapproximability results have been obtained from the parameterized perspective. This article surveys some of such results, with a focus on $k$-Clique, $k$-SetCover, and other related problems.
Let $BQP(n)$ be a boolean quadric polytope, $LOP(m)$ be a linear ordering polytope. It is shown that $BQP(n)$ is linearly isomorphic to a face of $LOP(2n)$.
The paper proposes a logical model of combinatorial problems, also it gives an example of a problem of the class NP that can not be solved in polynomial time on the dimension of the problem.
We define some notions of the decentralization of a deterministic input-output machine. This opens the possibility for introducing game-theoretic elements -- such as strategic players -- inside the machine, as part of its design.
We show that multiplication can be done in polynomial time on a three counter machine that receives its input as the contents of two counters. The technique is generalized to functions of two variables computable by deterministic Turing machines in linear space.
On example of tasks of class NP the questions concerning accuracy of work of already existing and possible in the future algorithms for the solution of tasks on discrete structures are considered.
Let $e_{1},\dots, e_{k}$ be complex $n\times n$ matrices such that $e_{i}e_{j}=-e_{j}e_{i}$ whenever $i\not=j$. We conjecture that $\hbox{rk}(e_{1}^{2})+\hbox{rk}(e_{2}^{2})+\cdots+\hbox{rk}(e_{k}^{2})\leq O(n\log n)$, and prove some results in this direction.