On representing the positive semidefinite cone using the second-order cone

The second-order cone plays an important role in convex optimization and has strong expressive abilities despite its apparent simplicity. Second-order cone formulations can also be solved more efficiently than semidefinite programming problems in general. We consider the following question, posed by Lewis and Glineur, Parrilo, Saunderson: is it possible to express the general positive semidefinite cone using second-order cones? We provide a negative answer to this question and show that the (Formula presented.) positive semidefinite cone does not admit any second-order cone representation. In fact we show that the slice consisting of (Formula presented.) positive semidefinite Hankel matrices does not admit a second-order cone representation. Our proof relies on exhibiting a sequence of submatrices of the slack matrix of the (Formula presented.) positive semidefinite cone whose “second-order cone rank” grows to infinity.Part of this work was done while the author was at Massachusetts Institute of Technology where he was supported by Grant AFOSR FA9550-11-1-030

Towards a Shared Vision on International Agricultural Research

Opening statement at the Global Forum on Agricultural Research held during CGIAR International Centers Week, October-November 1996, by IFAD President and GFAR Chairman Fawzi H. Al-Sulta

Semidefinite Approximations of the Matrix Logarithm

© 2018, SFoCM. The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with respect to the positive semidefinite order. This operator concavity property leads to numerous concavity and convexity results for other matrix functions, many of which are of importance in quantum information theory. In this paper we show how to approximate the matrix logarithm with functions that preserve operator concavity and can be described using the feasible regions of semidefinite optimization problems of fairly small size. Such approximations allow us to use off-the-shelf semidefinite optimization solvers for convex optimization problems involving the matrix logarithm and related functions, such as the quantum relative entropy. The basic ingredients of our approach apply, beyond the matrix logarithm, to functions that are operator concave and operator monotone. As such, we introduce strategies for constructing semidefinite approximations that we expect will be useful, more generally, for studying the approximation power of functions with small semidefinite representations

Breast Cancer in Geriatric Patients: Current Landscape and Future Prospects

Breast cancer is the most common cancer diagnosed among women worldwide and more than half are diagnosed above the age of 60 years. Life expectancy is increasing and the number of breast cancer cases diagnosed among older women are expected to increase. Undertreatment, mostly due to unjustifiable fears of advanced-age and associated comorbidities, is commonly practiced in this group of patients who are under-represented in clinical trials and their management is not properly addressed in clinical practice guidelines. With modern surgery and anesthesia, breast surgeries are considered safe and is usually associated with very low complication rates, regardless of extent of surgery. However, oncoplastic surgery and management of the axilla can be tailored based on patients\u27- and disease-related factors. Most of chemotherapeutic agents, along with targeted therapy and anti-Human epidermal growth factor receptor-2 (HER2) drugs can be safely given for older patients, however, dose adjustment and close monitoring of potential adverse events might be needed. The recently introduced cyclin-D kinase (CDK) 4/6-inhibitors in combination with aromatase inhibitors (AI) or fulvestrant, which changed the landscape of breast cancer therapy, are both safe and effective in older patients and had substituted more aggressive and potentially toxic interventions. Despite its proven efficacy, adjusting or even omitting adjuvant radiation therapy, at least in low-risk older patients, is safe and frequently practiced. In this paper, we review existing data related to breast cancer management among older patients across the continuum; from resection of the primary tumor through adjuvant chemotherapy, radiation and endocrine therapy up to the management of recurrent and advanced-stage disease

The Set of Separable States has no Finite Semidefinite Representation Except in Dimension 3 × 2

Given integers n $\geq$ m, let Sep(n,m) be the set of separable states on the Hilbert space $\mathbb{C}^n \otimes \mathbb{C}^m$. It is well-known that for (n,m)=(3,2) the set of separable states has a simple description using semidefinite programming: it is given by the set of states that have a positive partial transpose. In this paper we show that for larger values of n and m the set Sep(n,m) has no semidefinite programming description of finite size. As Sep(n,m) is a semialgebraic set this provides a new counterexample to the Helton-Nie conjecture, which was recently disproved by Scheiderer in a breakthrough result. Compared to Scheiderer's approach, our proof is elementary and relies only on basic results about semialgebraic sets and functions

Experimental study of heat transfer enhancement by inserting metal chain in heat exchanger tube

Heat transfer augmentation in heat exchangers is important in many large industrial applications and many studies have been conducted on this subject. In this paper, an experimental study was used to verify the increased heat transfer of a circular heat exchanger tube with the insertion of metal chains, under turbulent flow conditions. A rig was designed and fabricated to investigate the effects of using the metal chain as turbulators inside the heat exchanger pipe, on heat transfer performance and on fluid flow behavior. The metal chains used were of different lengths of chain ring and different diameters of ring wire. Five ring length/tube diameter ratios (P/D) were used, (1, 2, 3, 4 and 5). Two wire diameter /tube diameter ratios (t/D) were used in this work (0.1 and 0.15). Heavy fuel oil (HFO) was used inside the tube, flowing at 30 °C with uniform tube wall temperature. The Reynolds numbers tested were between 5,000 and 15,000. The results showed the thermal enhancement factor (η) decreased with increasing Reynolds number for all cases, depending on lengths of chain ring (P) and thickness the weir chain (t) values. A maximum thermal enhancement factor (η) was found with a metal chain at P/D=3 and t/D= 0.15. The results also show that P/D=1 and t= 4mm, give the highest Nusselt number

Resilient Back Propagation Algorithm for Breast Biopsy Classification Based on Artificial Neural Networks

Non

Larger Corner-Free Sets from Combinatorial Degenerations

There is a large and important collection of Ramsey-type combinatorial problems, closely related to central problems in complexity theory, that can be formulated in terms of the asymptotic growth of the size of the maximum independent sets in powers of a fixed small (directed or undirected) hypergraph, also called the Shannon capacity. An important instance of this is the corner problem studied in the context of multiparty communication complexity in the Number On the Forehead (NOF) model. Versions of this problem and the NOF connection have seen much interest (and progress) in recent works of Linial, Pitassi and Shraibman (ITCS 2019) and Linial and Shraibman (CCC 2021). We introduce and study a general algebraic method for lower bounding the Shannon capacity of directed hypergraphs via combinatorial degenerations, a combinatorial kind of "approximation" of subgraphs that originates from the study of matrix multiplication in algebraic complexity theory (and which play an important role there) but which we use in a novel way. Using the combinatorial degeneration method, we make progress on the corner problem by explicitly constructing a corner-free subset in $F_2^n \times F_2^n$ of size $\Omega(3.39^n/poly(n))$, which improves the previous lower bound $\Omega(2.82^n)$ of Linial, Pitassi and Shraibman (ITCS 2019) and which gets us closer to the best upper bound $4^{n - o(n)}$. Our new construction of corner-free sets implies an improved NOF protocol for the Eval problem. In the Eval problem over a group $G$, three players need to determine whether their inputs $x_1, x_2, x_3 \in G$ sum to zero. We find that the NOF communication complexity of the Eval problem over $F_2^n$ is at most $0.24n + O(\log n)$, which improves the previous upper bound $0.5n + O(\log n)$.Comment: A short version of this paper will appear in the proceedings of ITCS 2022. This paper improves results that appeared in arxiv:2104.01130v