Fairness in Multiuser Systems with Polymatroid Capacity Region

For a wide class of multi-user systems, a subset of capacity region which includes the corner points and the sum-capacity facet has a special structure known as polymatroid. Multiaccess channels with fixed input distributions and multiple-antenna broadcast channels are examples of such systems. Any interior point of the sum-capacity facet can be achieved by time-sharing among corner points or by an alternative method known as rate-splitting. The main purpose of this paper is to find a point on the sum-capacity facet which satisfies a notion of fairness among active users. This problem is addressed in two cases: (i) where the complexity of achieving interior points is not feasible, and (ii) where the complexity of achieving interior points is feasible. For the first case, the corner point for which the minimum rate of the active users is maximized (max-min corner point) is desired for signaling. A simple greedy algorithm is introduced to find the optimum max-min corner point. For the second case, the polymatroid properties are exploited to locate a rate-vector on the sum-capacity facet which is optimally fair in the sense that the minimum rate among all users is maximized (max-min rate). In the case that the rate of some users can not increase further (attain the max-min value), the algorithm recursively maximizes the minimum rate among the rest of the users. It is shown that the problems of deriving the time-sharing coefficients or rate-spitting scheme can be solved by decomposing the problem to some lower-dimensional subproblems. In addition, a fast algorithm to compute the time-sharing coefficients to attain a general point on the sum-capacity facet is proposed.Comment: Submitted To IEEE Transactions on Information Theory, June 200

Throughput Scaling Laws for Wireless Networks with Fading Channels

A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. It is assumed that each link can be active and transmit with a constant power P or remain silent. The objective is to maximize the throughput over the selection of active links. By deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading (i) the maximum throughput scales like $\log n$ (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links by a chi-squared random variable. To obtain the lower bound, a decentralized link activation strategy is proposed and analyzed.Comment: Submitted to IEEE Transactions on Information Theory (Revised

Wegner estimate and level repulsion for Wigner random matrices

We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. Under suitable assumptions on the distribution of the single matrix element, we first prove that, away from the spectral edges, the empirical density of eigenvalues concentrates around the Wigner semicircle law on energy scales $\eta \gg N^{-1}$. This result establishes the semicircle law on the optimal scale and it removes a logarithmic factor from our previous result \cite{ESY2}. We then show a Wegner estimate, i.e. that the averaged density of states is bounded. Finally, we prove that the eigenvalues of a Wigner matrix repel each other, in agreement with the universality conjecture.Comment: 35 pages, LateX fil

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

Privacy-Preserving Methods for Sharing Financial Risk Exposures

Unlike other industries in which intellectual property is patentable, the financial industry relies on trade secrecy to protect its business processes and methods, which can obscure critical financial risk exposures from regulators and the public. We develop methods for sharing and aggregating such risk exposures that protect the privacy of all parties involved and without the need for a trusted third party. Our approach employs secure multi-party computation techniques from cryptography in which multiple parties are able to compute joint functions without revealing their individual inputs. In our framework, individual financial institutions evaluate a protocol on their proprietary data which cannot be inverted, leading to secure computations of real-valued statistics such a concentration indexes, pairwise correlations, and other single- and multi-point statistics. The proposed protocols are computationally tractable on realistic sample sizes. Potential financial applications include: the construction of privacy-preserving real-time indexes of bank capital and leverage ratios; the monitoring of delegated portfolio investments; financial audits; and the publication of new indexes of proprietary trading strategies

Associations between Tumor Vascularity, Vascular Endothelial Growth Factor Expression and PET/MRI Radiomic Signatures in Primary Clear-Cell–Renal-Cell-Carcinoma: Proof-of-Concept Study

Studies have shown that tumor angiogenesis is an essential process for tumor growth, proliferation and metastasis. Also, tumor angiogenesis is an important prognostic factor of clear cell renal cell carcinoma (ccRCC), as well as a factor in guiding treatment with antiangiogenic agents. Here, we attempted to find the associations between tumor angiogenesis and radiomic imaging features from PET/MRI. Specifically, sparse canonical correlation analysis was conducted on 3 feature datasets (i.e., radiomic imaging features, tumor microvascular density (MVD), and vascular endothelial growth factor (VEGF) expression) from 9 patients with primary ccRCC. In order to overcome the potential bias of intratumoral heterogeneity of angiogenesis, this study investigated the relationship between regional expressions of angiogenesis and VEGF, and localized radiomic features from different parts within the tumors. Our study highlighted the significant strong correlations between radiomic features and MVD, and also demonstrated that the spatiotemporal features extracted from DCE-MRI provided stronger radiomic correlation to MVD than the textural features extracted from Dixon sequences and FDG PET. Furthermore, PET/MRI, which takes advantage of the combined functional and structural information, had higher radiomics correlation to MVD than solely utilizing PET or MRI alone

Alternate Metabolic Programs Define Regional Variation of Relevant Biological Features in Renal Cell Carcinoma Progression

ccRCC has recently been redefined as a highly heterogeneous disease. In addition to genetic heterogeneity, the tumor displays risk variability for developing metastatic disease, therefore underscoring the urgent need for tissue-based prognostic strategies applicable to the clinical setting. We’ve recently employed the novel positron emission tomography/magnetic resonance (PET/MR) image modality to enrich our understanding of how tumor heterogeneity can relate to gene expression and tumor biology to assist in defining individualized treatment plans

Use of Yttrium-90 Microspheres in Patients with Advanced Hepatocellular Carcinoma and Portal Vein Thrombosis

Patients with portal vein thrombosis (PVT) and hepatocellular carcinoma (HCC) have limited treatment options due to increased disease burden and diminished hepatic perfusion. 90Y-microspheres may be better tolerated than chemoembolization in these patients. Here we review the safety and efficacy of 90Y-microsphere use for HCC with major PVT