Finding the Median (Obliviously) with Bounded Space

We prove that any oblivious algorithm using space $S$ to find the median of a list of $n$ integers from $\{1,...,2n\}$ requires time $\Omega(n \log\log_S n)$. This bound also applies to the problem of determining whether the median is odd or even. It is nearly optimal since Chan, following Munro and Raman, has shown that there is a (randomized) selection algorithm using only $s$ registers, each of which can store an input value or $O(\log n)$-bit counter, that makes only $O(\log\log_s n)$ passes over the input. The bound also implies a size lower bound for read-once branching programs computing the low order bit of the median and implies the analog of $P \ne NP \cap coNP$ for length $o(n \log\log n)$ oblivious branching programs

Circuits with Medium Fan-In

We consider boolean circuits in which every gate may compute an arbitrary boolean function of k other gates, for a parameter k. We give an explicit function $f:{0,1}^n -> {0,1} that requires at least Omega(log^2(n)) non-input gates when k = 2n/3. When the circuit is restricted to being layered and depth 2, we prove a lower bound of n^(Omega(1)) on the number of non-input gates. When the circuit is a formula with gates of fan-in k, we give a lower bound Omega(n^2/k*log(n)) on the total number of gates. Our model is connected to some well known approaches to proving lower bounds in complexity theory. Optimal lower bounds for the Number-On-Forehead model in communication complexity, or for bounded depth circuits in AC_0, or extractors for varieties over small fields would imply strong lower bounds in our model. On the other hand, new lower bounds for our model would prove new time-space tradeoffs for branching programs and impossibility results for (fan-in 2) circuits with linear size and logarithmic depth. In particular, our lower bound gives a different proof for a known time-space tradeoff for oblivious branching programs

Humanitarian “Reversing” in the Education Development in the Russian Federation Education under the Conditions of Transhumanistic Challenges in the Era of Globalisation

The effectiveness of the development of individual countries within the conditions of accelerating scientific and technological progress, expanding the influence of globalisation and integration processes in the global socio-cultural space are very important during the exchange of international students. The purpose of the paper is to research the methodological foundations of the humanities education for international students as an alternative to transhumanist ideology. In the framework of general scientific research methods, a paradigmatic approach is used as a factor analysis of students' educational processes. Particular attention is paid to the substantiation of the methodological foundations of the education humanisation on the basis of modern ontologically anthropological and religious-anthropological achievements of the philosophical field of knowledge. In this regard, the thesis is accepted that the artificially imposed transhumanist ideology performs a key integrating function when considering the practice of education of international students. The novelty of the study is due to a discussion of the contradictions caused by all-round technocratisation and informatisation, the fall of moral standards, and the degradation of human behavior. The practical significance of the study is determined by the need to develop a different pedagogy and model of education for modern students

Quantum vs. Classical Read-once Branching Programs

The paper presents the first nontrivial upper and lower bounds for (non-oblivious) quantum read-once branching programs. It is shown that the computational power of quantum and classical read-once branching programs is incomparable in the following sense: (i) A simple, explicit boolean function on 2n input bits is presented that is computable by error-free quantum read-once branching programs of size O(n^3), while each classical randomized read-once branching program and each quantum OBDD for this function with bounded two-sided error requires size 2^{\Omega(n)}. (ii) Quantum branching programs reading each input variable exactly once are shown to require size 2^{\Omega(n)} for computing the set-disjointness function DISJ_n from communication complexity theory with two-sided error bounded by a constant smaller than 1/2-2\sqrt{3}/7. This function is trivially computable even by deterministic OBDDs of linear size. The technically most involved part is the proof of the lower bound in (ii). For this, a new model of quantum multi-partition communication protocols is introduced and a suitable extension of the information cost technique of Jain, Radhakrishnan, and Sen (2003) to this model is presented.Comment: 35 pages. Lower bound for disjointness: Error in application of info theory corrected and regularity of quantum read-once BPs (each variable at least once) added as additional assumption of the theorem. Some more informal explanations adde

A Postcolonial Critique of Industrial Design: A critical evaluation of the relationship of culture and hegemony to design practice and education since the late 20th century.

A Postcolonial Critique of Industrial Design: A critical evaluation of the relationship of culture and hegemony to design practice and education since the late 20th century. This thesis specifically focuses on the professional practices and training of Western industrial designers using postcolonial theory to inform working practices in a complex global ecology. It investigates the culturally hegemonic construction of design solutions in man-made products. By adopting key ideas from postcolonial and cultural studies as a lens to evaluate fields of industrial design discourse, practice and pedagogy, the work proceeds from the premise that design is not intrinsic to a product but the result of a myriad different forces and factors acting on it externally including hegemonic potencies. By reinterpreting technological formations in light of research emerging from post-colonial studies, it attempts to broaden our intellectual understanding of how product design in theory, practice and education can often rely upon western [hegemonic] aesthetic and deep cultural archetypes. The purpose of this enquiry is to highlight the potentials that exist to explore a synergy between east and west in industrial design with a prospective vision for global, trans-cultural design. The research claims that current design practice often leads to culturally determined - rather than universal - conceptions in design and it attempts to re-conceptualise design as practice within a necessarily hegemonic culture. This hegemony needs to be acknowledged and redressed via increased awareness and changes to the intellectual heritage and autonomy of West European and American industrial design, in its dialogue, practice and education. As an epistemological project to identify knowledge within this discourse, it suggests new methodological and strategic approaches to engage with the crisis the discipline faces in light of globalisation so as to open up future discussions in design discourse and give a voice to the many silences that make up the noise of the world. It attempts to: • Further understand the trajectory of hegemony and globalisation in relation to design, technology and culture. • Critically engage with cross- and trans-cultural, global and social design implications. • Address the discrepancies between designers’ culture and users’ culture, to expose the necessity for more culturally-cognizant design practice and pedagogic provision. The research was initiated by identifying a number of questions that designers and users may consciously or subconsciously confront when faced with products that problematise the imagined universal values of designed products in terms of gender and culture. It explores how certain design solutions produced and developed in the west and their diffusion into global, international markets and foreign cultures could affect those cultures by asking in what ways the usability, aesthetic and symbolic characteristics of these artefacts often unwittingly contribute to the privilege or marginalisation of people from particular socio-cultural backgrounds. The thesis intervention is that product designers are neither explicitly trained to comprehend nor surmount their respective cultural constraints and design education both nationally and internationally is not sufficiently equipped with the tools to acknowledge and confront this. The key arguments presented in this thesis are: 1. Products can often be deconstructed to identify cultural connotations or omissions in their design. 2. Global, a-cultural design and universal usability are fallacies that frequently deny the existence of an underlying cultural hegemony at play. 3. Mass-produced products can gradually homogenise and eradicate cultural diversity contributing to the negative effects of colonialist attitudes and/or globalisation. 4. Academia and educational institutions have the potential to extend awareness in this field to inform and train future designers and graduates to better advance design obligations in global, trans-cultural, cross-cultural and multicultural contexts.University of Wale