The introduction to this works states that in an information society “free flow of information is a fundamental principle for bridging the knowledge gaps between privileged and under‐privileged communities”. Open access (OA) takes that principle to scholarly communication with the vision that potential readers and users should be freely able to read, download, copy, distribute, print, search or link to, the full text of works, without financial cost or legal or technical barriers. OA can be achieved in a number of ways, the most common of which are to post work to a web site or place in an institutional, disciplinary or national digital repository, commonly called self‐archiving or to publish in an open access journal.
Open Access to Knowledge and Information opens with a summary of some of the major open access statements or declarations from around the world at the time of publication. It informs the reader of the role and responsibilities of the National Knowledge Council (NKC) of India which runs a working group on open access and open education resources. NKC has recommended and supported knowledge portals in key sectors such as water and energy. There are many similar bodies in the region supporting open access and the book strives to illustrate some of the South Asian open access initiatives currently under way. The book contains sections listing and briefly describing a selection of digital library and open courseware initiatives, national and institutional repositories, open access journals and metadata harvesting services. Each entry briefly describes the type of initiative, the implementing agency, supporting agencies, allied projects, software used, web address and a brief description of resources included. The inclusion of the web address makes one wonder whether perhaps HTML would have been a better delivery mechanism than PDF, although the PDF is handy for libraries who may wish to print out a copy for their shelves.
It is not clear to the reader if the open access initiatives reported are the total number of initiatives at the time of publication, or perhaps a selected sample. If they are a sample; on what basis they were selected? There are also some small grammatical and typesetting errors, for example page 14 finishes mid‐sentence and the sentence is not continued on page 15. In addition, the volume would benefit from an index.
That said, some very interesting open access initiatives are reported. National repositories such as The Librarians' Digital Library which collects and disseminates articles, conference papers, theses, reports and has a self‐archiving facility for registered users; and OpenMED, an initiative to encourage self‐archiving among Biomedical researchers are examples. Similarly interesting institutional repositories such as the Indian Institute of Science's Research Publications Repository and their Electronic Thesis and Dissertations Repository are described.
This volume goes beyond scholarly publishing and reports open access digital libraries that are working to provide open access to South Asian documentary heritage items such as the Archives of Indian Labour, and the Digital e‐library where the mission is to be an “Internet enabled Mobile Digital Library brought to use of common citizen for promoting literacy”. Some resources listed in the work are not truly open access, or are at least not openly accessible to this reader in Australia, such as the HEC National Digital Library in Pakistan. Some items in their collection are OA, for example the theses and dissertations, but others require a login and password. This mislabeling does not diminish the excellent work performed by this Digital library in facilitating access to peer reviewed journals, online databases and e‐books to researchers in Pakistan's university and research sector.
The book concludes with the acknowledgement that open access has far to go in South Asia (indicating that South Asia has much in common with the rest of the world in this regard). It brings to the readers' attention some of the interesting and useful open access initiatives that are underway in South Asia at the present time, thus increasing their visibility, accessibility and global recognition. Furthermore, the book practices what it preaches, being freely available online as an open access e‐book from: http://unesdoc.unesco.org/images/0015/001585/158585e.pdf
We begin by investigating the uniqueness of an optimal mass transport problem with $N$ marginals for $N\geq 3$ by transforming it into a lower marginal optimal transportation problem. Specifically, for a family of probability spaces $\{(X_k,\mathcal{B}_{X_k},\mu_k)\}_{k=1}^N$ and a cost function $c: X_1\times\cdots\times X_N\to \mathbb{R}$, we consider \[\tag{\textbf{MKP}}\label{T1} \inf_{\lambda\in\Pi(\mu_1,\ldots,\mu_N)}\int_{\prod_{k=1}^N X_k}c\,d\lambda. \] Then, for each ordered subset $\mathcal{P} of \{1,...,N\}$, we create a new cost function $c_\mathcal{P}$ corresponding to the original cost function $c$ defined on $\prod_{k=1}^p X_{i_k}$. This new cost function $c_\mathcal{P}$ possesses many of the features of the original cost $c$, while having the property that any optimal plan $\lambda$ of \eqref{T1} restricted to $\prod_{k=1}^p X_{i_k}$ is also an optimal plan to the problem \[\label{T2} \inf_{\tau\in\Pi(\mu_{i_1},\ldots\mu_{i_p})}\int_{\prod_{k=1}^p X_{i_k}}c_{\mathcal{P}}\,d\tau. \] Our main contribution is to demonstrate that, for appropriate choices of the index set $\mathcal{P}$, one can recover the optimal plans of \eqref{T1} from \eqref{T2}. We examine situations in which the problem \eqref{T1} admits a unique solution depending on the uniqueness of the solution for the lower marginal problems of the form \eqref{T2}. This allows us to establish numerous uniqueness results for multi-marginal problems, even when the unique optimal plan is not necessarily induced by a map. To achieve this, we extensively employ disintegration theorems and the $c$-extremality notions. Furthermore, we demonstrate several new applications to illustrate the applicability of this approach. Next, we deal with the case $N=2$. For $X,Y\subseteq\mathbb{R}^{n+1}$, for Borel probability spaces $(X,\mathcal{B}_X,\mu)$ and $(Y,\mathcal{B}_Y,\nu)$ and the cost $c:X\times Y\to\mathbb{R}$, we study \[\tag{\textbf{2-MKP}}\label{T3} \inf\left\{\int_{X\times Y} c(x,y)\,d\lambda\ :\ \lambda \in\Pi(\mu,\nu) \right\}. \] We first consider an optimal transport problem with a multi-layers target space for the cost $c(x,y)=h(x-y)$ with $h$ being strictly convex and differentiable. Namely, we assume \[ X=\overline{X}\times\{\overline{x}\},\quad\text{and}\quad Y=\bigcup_{k=1}^K \left(\overline{Y}_{k}\times \{\overline{y}_k\}\right), \] We also assume that $\mu|_{\overline{X}}\ll\mathcal{L}^n$, but $\mu\perp\mathcal{L}^{n+1} $. We show that for $K\geq 2$, the solution to \eqref{T3} is unique but it concentrates on the graph of several maps. Secondly, for general closed subsets $X\subseteq \mathbb{R}^{n+1}$, we consider the case where the first marginal of the form \[ \int_X f(x)\,d\mu(x)=\int_X f(x)\alpha(x)\,d\mathcal{L}^{n+1}(x)+\int_{X_0} f(x_0)\, d S(x_0),\quad \forall f\in C_b(X), \] where $X_0\subseteq X$ is an $n$-dimensional manifold.
