PolarStar: Expanding the Scalability Horizon of Diameter-3 Networks

In this paper, we present PolarStar, a novel family of diameter-3 network topologies derived from the star product of two low-diameter factor graphs. The proposed PolarStar construction gives the largest known diameter-3 network topologies for almost all radixes. When compared to state-of-the-art diameter-3 networks, PolarStar achieves 31% geometric mean increase in scale over Bundlefly, 91% over Dragonfly, and 690% over 3-D HyperX. PolarStar has many other desirable properties including a modular layout, large bisection, high resilience to link failures and a large number of feasible sizes for every radix. Our evaluation shows that it exhibits comparable or better performance than other diameter-3 networks under various traffic patterns.Comment: 13 pages, 13 figures, 4 table

The Hamiltonian formulation of General Relativity: myths and reality

A conventional wisdom often perpetuated in the literature states that: (i) a 3+1 decomposition of space-time into space and time is synonymous with the canonical treatment and this decomposition is essential for any Hamiltonian formulation of General Relativity (GR); (ii) the canonical treatment unavoidably breaks the symmetry between space and time in GR and the resulting algebra of constraints is not the algebra of four-dimensional diffeomorphism; (iii) according to some authors this algebra allows one to derive only spatial diffeomorphism or, according to others, a specific field-dependent and non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac [Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in "Gravitation: An Introduction to Current Research" (1962) 227] of the canonical structure of GR are equivalent. We provide some general reasons why these statements should be questioned. Points (i-iii) have been shown to be incorrect in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation of GR. We also demonstrate that ADM and Dirac formulations are related by a transformation of phase-space variables from the metric $g_{\mu\nu}$ to lapse and shift functions and the three-metric $g_{km}$, which is not canonical. This proves that point (iv) is incorrect. Points (i-iii) are mere consequences of using a non-canonical change of variables and are not an intrinsic property of either the Hamilton-Dirac approach to constrained systems or Einstein's theory itself.Comment: References are added and updated, Introduction is extended, Subsection 3.5 is added, 83 pages; corresponds to the published versio

Molecular Targeted Therapies of Aggressive Thyroid Cancer

Differentiated thyroid carcinomas (DTCs) that arise from follicular cells account >90% of thyroid cancer (TC) [papillary thyroid cancer (PTC) 90%, follicular thyroid cancer (FTC) 10%], while medullary thyroid cancer (MTC) accounts <5%. Complete total thyroidectomy is the treatment of choice for PTC, FTC, and MTC. Radioiodine is routinely recommended in high-risk patients and considered in intermediate risk DTC patients. DTC cancer cells, during tumor progression, may lose the iodide uptake ability, becoming resistant to radioiodine, with a significant worsening of the prognosis. The lack of specific and effective drugs for aggressive and metastatic DTC and MTC leads to additional efforts toward the development of new drugs. Several genetic alterations in different molecular pathways in TC have been shown in the past few decades, associated with TC development and progression. Rearranged during transfection (RET)/PTC gene rearrangements, RET mutations, BRAF mutations, RAS mutations, and vascular endothelial growth factor receptor 2 angiogenesis pathways are some of the known pathways determinant in the development of TC. Tyrosine kinase inhibitors (TKIs) are small organic compounds inhibiting tyrosine kinases auto-phosphorylation and activation, most of them are multikinase inhibitors. TKIs act on the aforementioned molecular pathways involved in growth, angiogenesis, local, and distant spread of TC. TKIs are emerging as new therapies of aggressive TC, including DTC, MTC, and anaplastic thyroid cancer, being capable of inducing clinical responses and stabilization of disease. Vandetanib and cabozantinib have been approved for the treatment of MTC, while sorafenib and lenvatinib for DTC refractory to radioiodine. These drugs prolong median progression-free survival, but until now no significant increase has been observed on overall survival; side effects are common. New efforts are made to find new more effective and safe compounds and to personalize the therapy in each TC patient

Problems relating to arcs in projective space and subrings in Z^n

An important problem in mathematics is understanding the behavior of functions. If we can show that complicated functions can be simplified, computation becomes more feasible. In this thesis, we describe two major projects: counting arcs in projective space and counting subrings in $\Z^n$. In the case of arcs in \mb{P}^{k-1}(\Fq), we seek to understand whether the counting function can be expressed by a simple formula like a polynomial. In the case of subrings of $\Z^n$, we are interested in the asymptotic growth of the function that counts subrings of index at most $X$. An $n$-arc in $(k-1)$-dimensional projective space is a set of $n$ points so that no $k$ lie on a hyperplane. Let $C_{n,k}(q)$ be the number of $n$-arcs in \mb{P}^{k-1}(\Fq). We discuss new results for $n$-arcs when $k = 3$ and 4. Building off work of Kaplan, Kimport, Lawrence, Peilen, and Weinreich, we show that $C_{10,3}(q)$ is not quasipolynomial in $q$. For almost all $n$, no formulas for $C_{n,k}(q)$ were known when $k \ge 4$. We introduce a new algorithm to count $n$-arcs in \mb{P}^3(\Fq) in terms of a small number of special combinatorial objects and use it to compute $C_{n,4}(q)$ for $n \le 7$. Finally, we discuss generalizations of this algorithm to higher-dimensional projective space.Let $f_n(p^e)$ count the number of subrings of index $p^e$ in $\Z^n$. We study lower bounds for $f_n(p^e)$ using techniques from combinatorics and arithmetic geometry. Using these lower bounds, we give the best known result about the asymptotic growth of subrings in $\Z^n$ when $n \ge 8$ by studying the analytic properties of the subring zeta function for $\Z^n$. These results immediately give new information about the asymptotic growth of orders in a fixed degree $n$ number field. Finally, we consider the behavior of $f_n(p^e)$ as a function of $p$. We give evidence that this function may always be polynomial in $p$

Teaching note:personal attack or the personal touch? Evaluating the use of video feedback methods with qualifying social workers

Social work skills such as the ability to reflect on self and to recognize and manage emotions are fostered in part through using and receiving feedback, however there is limited research about feedback methods that effectively enable social work students and post-qualifying workers to engage with the emotional aspects of learning and feedback. This teaching note reports on a pilot project in which video feedback on academic assignments was provided to first year undergraduate social work students studying at a university in England. The project findings underscore the importance of engaging with the emotional dimensions of feedback processes and recognizing how feedback experiences can shape emerging learner and professional identities. The findings also underline the psychological and social skills required to engage in more performative aspects of contemporary education and practice. We argue that social work students are likely to benefit from support to develop meta-cognition (the process of thinking about one’s thinking processes) and self-regulation (regulation of emotion and behavior) skills before they can make sense of academic and practice-orientated feedback. Video feedback on academic assignments is therefore best utilized when it is underpinned by a dialogical approach to teaching and learning in the ‘classroom’ and the ‘field’