Computing the channel capacity of a communication system affected by uncertain transition probabilities

We study the problem of computing the capacity of a discrete memoryless channel under uncertainty affecting the channel law matrix, and possibly with a constraint on the average cost of the input distribution. The problem has been formulated in the literature as a max-min problem. We use the robust optimization methodology to convert the max-min problem to a standard convex optimization problem. For small-sized problems, and for many types of uncertainty, such a problem can be solved in principle using interior point methods (IPM). However, for large-scale problems, IPM are not practical. Here, we suggest an $\mathcal{O}(1/T)$ first-order algorithm based on Nemirovski (2004) which is applied directly to the max-min problem.Comment: 22 pages, 2 figure

Oracle-Based Robust Optimization via Online Learning

Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the problem solved is a min-max problem where a solution is judged according to its performance on the worst possible realization of the parameters. In many cases, a straightforward solution of the robust optimization problem of a certain type requires solving an optimization problem of a more complicated type, and in some cases even NP-hard. For example, solving a robust conic quadratic program, such as those arising in robust SVM, ellipsoidal uncertainty leads in general to a semidefinite program. In this paper we develop a method for approximately solving a robust optimization problem using tools from online convex optimization, where in every stage a standard (non-robust) optimization program is solved. Our algorithms find an approximate robust solution using a number of calls to an oracle that solves the original (non-robust) problem that is inversely proportional to the square of the target accuracy

Young patients with cancer and a digital social network: the voice beyond the clinic.

INTRODUCTION: Digital social networks have become a key player in the ecosystem of young patients with cancer, with regard to their unique perspectives and unmet needs. This study aims to investigate the web-based social community tools and to characterise the user profile, unmet needs and goals of young patients with cancer. METHODS: A web-based survey was distributed via large-scale social network designated for young patients with cancer (age 18-45 years) Stop Cancer. The survey collected demographic data and oncological status. Primary outcome was potential goals of accessing the network; secondary outcomes were emotional impact, effect of disease status, education, marital status and employment, on user satisfaction rate. RESULTS: The survey was available for 5 days (10/2018) and was filled by 523 participants. Breast cancer, haematological malignancies and colorectal cancer were the most common diagnoses. The majority had non-metastatic disease at diagnosis, 79% had no evidence of disease at time of the survey. Forty-five per cent considered the network as a reliable source for medical information. Academic education was associated with higher satisfaction from the platform. There were no differences between cancer survivors and patients with active disease in patterns of platform usage. The social network had an allocated section for 'patient mentoring' of newly diagnosed members by survivors. DISCUSSION: Our study portrayed the user prototype of a social digital network among young adult patients with cancer, indicating challenging trends. Whereas social media may prove a powerful tool for patients and physicians alike, it may also serve as a research tool to appraise wide practices within a heterogeneous population. Nevertheless, it acts as a double-edged sword in the setting of uncontrolled medical information. It is our role as healthcare providers to join this race and play an active role in shaping its medical perspectives

Ordered Incidence geometry and the geometric foundations of convexity theory

An Ordered Incidence Geometry, that is a geometry with certain axioms of incidence and order, is proposed as a minimal setting for the fundamental convexity theorems, which usually appear in the context of a linear vector space, but require only incidence, order (and for separation, completeness), and none of the linear structure of a vector space.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42995/1/22_2005_Article_BF01227810.pd

DUALITY AND EQUILIBRIUM PRICES IN ECONOMICS OF UNCERTAINTY

Abstract. A random variable (RV) X is given a minimum selling price (S) SU (X) := sup x {x + EU (X − x)} and a maximum buying price where U (·) and P (·) are appropriate functions. These prices are derived from considerations of stochastic optimization with recourse, and are called recourse certainty equivalents (RCE's) of X. Both RCE's compute the "value" of a RV as an optimization problem, and both problems (S) and (B) have meaningful dual problems, stated in terms of the Csiszár φ-divergence qi φ pi qi a generalized entropy function, measuring the distance between RV's with probability vectors p and q. The RCE SU was introduced i

A recourse certainty equivalent for decisions under uncertainty

http://deepblue.lib.umich.edu/bitstream/2027.42/3544/5/bal7898.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/3544/4/bal7898.0001.001.tx