On the expected diameter, width, and complexity of a stochastic convex-hull

We investigate several computational problems related to the stochastic convex hull (SCH). Given a stochastic dataset consisting of $n$ points in $\mathbb{R}^d$ each of which has an existence probability, a SCH refers to the convex hull of a realization of the dataset, i.e., a random sample including each point with its existence probability. We are interested in computing certain expected statistics of a SCH, including diameter, width, and combinatorial complexity. For diameter, we establish the first deterministic 1.633-approximation algorithm with a time complexity polynomial in both $n$ and $d$. For width, two approximation algorithms are provided: a deterministic $O(1)$-approximation running in $O(n^{d+1} \log n)$ time, and a fully polynomial-time randomized approximation scheme (FPRAS). For combinatorial complexity, we propose an exact $O(n^d)$-time algorithm. Our solutions exploit many geometric insights in Euclidean space, some of which might be of independent interest

Speeding up Thermalisation via Open Quantum System Variational Optimisation

Optimizing open quantum system evolution is an important step on the way to achieving quantum computing and quantum thermodynamic tasks. In this article, we approach optimisation via variational principles and derive an open quantum system variational algorithm explicitly for Lindblad evolution in Liouville space. As an example of such control over open system evolution, we control the thermalisation of a qubit attached to a thermal Lindbladian bath with a damping rate $\gamma$. Since thermalisation is an asymptotic process and the variational algorithm we consider is for fixed time, we present a way to discuss the potential speedup of thermalisation that can be expected from such variational algorithms.Comment: 10 pages, 4 figures, comments welcom

Recovery of Niobium and Tantalum from Low Grade Tin Slag - A Hydrometallurgical Approach

.Niobium and tantalum are known to co-occur with cassiterite deposits.During the process of extraction of tin by cassiterite smelting, these metals join the slag phase and the slag is processed for the recovery of niobium and tantalum. The processed slag rich in niobium and tantalum is digested with hydrofluric acid, and subjected to solvent extraction for the removal of additional impurities as well as for the separation of niobium and tantalum. This paper reports on the upgradation of tin slag typically containing 3.4% Nb205 and 3.0% Ta205 by a combination of chemical treatments. In the process, unwanted associations in the slag viz. alumina, silica, calcia, iron oxide etc., are selectively solubilized by a sequential treatment with alkali and acid leaching leaving a residue containing 10.6% Nb205 and 10.4% Ta205 with a recovery of 86.5 and 95.5% respectively. The product represents an enrichment of about 3.24 times and was found to be suitable for the extraction of niobium and tantalum by HF-H2SO4 dissolution

MINA: {C}onvex Mixed-Integer Programming for Non-Rigid Shape Alignment

We present a convex mixed-integer programming formulation for non-rigid shape matching. To this end, we propose a novel shape deformation model based on an efficient low-dimensional discrete model, so that finding a globally optimal solution is tractable in (most) practical cases. Our approach combines several favourable properties: it is independent of the initialisation, it is much more efficient to solve to global optimality compared to analogous quadratic assignment problem formulations, and it is highly flexible in terms of the variants of matching problems it can handle. Experimentally we demonstrate that our approach outperforms existing methods for sparse shape matching, that it can be used for initialising dense shape matching methods, and we showcase its flexibility on several examples

Production of Ferromolybdenum from Indian Resources

In India, the resources of molybdenum are limited - primary sources are very low grade molysulphide deposits, molybdenum in low concentration co-occurs with copper and uranium deposits, processing of such deposits for copper and uranium yields small quantities of low grade molysulphide concentrate. Besides these, some quantities of molybdenum scrap andmolybdenum bearing effluents are generated as secondary sources in the countrv. This paper is concerned with the development of processes for treating these indigenous sources. Thefirst part of the paper describes the chemical processes for preparing pure compounds of molybdenum which could be utilized as starting materials for various metallurgical products of molybdenum. The second part of the paper deals with the production of ferroma! bdenum using these molybdenum intermediate compounds

Approximately-Strategyproof and Tractable Multi-Unit Auctions

We present an approximately-efficient and approximately-strategyproof auction mechanism for a single-good multiunit allocation problem. The bidding language allows marginal-decreasing piecewise-constant curves and quantity-based side constraints. We develop a fully polynomial-time approximation scheme for the multiunit allocation problem, which computes a (1+ε) approximation in worst-case time T=O(n3/ε), given n bids each with a constant number of pieces. We integrate this approximation scheme within a Vickrey–Clarke–Groves (VCG) mechanism and compute payments for an asymptotic cost of O(T log n). The maximal possible gain from manipulation to a bidder in the combined scheme is bounded by εV/(1+ε), where V is the total surplus in the efficient outcome.Engineering and Applied Science