Stable Matching: Choosing Which Proposals to Make

Why does stable matching work well in practice despite agents only providing short preference lists? Perhaps the most compelling explanation is due to Lee (Lee, 2016). He considered a model with preferences based on correlated cardinal utilities. The utilities were based on common public values for each agent and individual private values. He showed that for suitable utility functions, in large markets, for most agents, all stable matchings yield similar valued utilities. By means of a new analysis, we strengthen this result, showing that in large markets, with high probability, for \emph{all} but the bottommost agents, all stable matches yield similar valued utilities. We can then deduce that for \emph{all} but the bottommost agents, relatively short preference lists suffice. Our analysis shows that the key distinction is between models in which the derivatives of the utility function are bounded, and those in which they can be unbounded. For the bounded derivative model, we show that for any given constant $c\ge 1$, with $n$ agents on each side of the market, with probability $1 - n^{-c}$, for each agent its possible utilities in all stable matches vary by at most $O((c\ln n/n)^{1/3})$ for all but the bottommost $O((c\ln n/n)^{1/3})$ fraction of the agents. When the derivatives can be unbounded, we obtain the following bound on the utility range and the bottommost fraction: for any constant $\epsilon>0$, for large enough $n$, the bound is $\epsilon$. Both these bounds are tight. In the bounded derivative model, we also show the existence of an $\epsilon$-Bayes-Nash equilibrium in which agents make relatively few proposals. Our results all rely on a new technique for sidestepping the conditioning between the matching events that occur over the course of a run of the Deferred Acceptance algorithm. We complement these theoretical results with a variety of simulation experiments.Comment: 52 page

New perspectives in modified Gleason’s grading for prostatic cancer and its comparison with original Gleason’s

Background: The Gleason score is the most widely accepted histopathological grading system for prostate cancer since decade despite having many deficiency that can potentially impact patient health care. So ISUP agreed on developing a system of prognostic grade groups from I-V. Aim and objective was to study the new perspectives of modified Gleason’s grading and to compare it with original Gleason’s System with focus on the prognostic significance of the modifications.Methods: A retrospective study of 60 patients, who underwent TURP and Sextant biopsy and diagnosed as prostatic carcinoma in our institute were included in this study. Laboratory requisition forms with clinical history, PSA levels and histopathology reports of these patients were reviewed and graded accordingly to the newer gleasons. New Gleason grade includes five distinct Grade Groups based on the modified Gleason score groups. Grade Group 1 = Gleason score ≤6, Grade Group 2 = Gleason score 3 + 4 = 7, Grade Group 3 = Gleason score 4 + 3 = 7, Grade Group 4 = Gleason score 8, Grade Group 5 = Gleason scores 9 and 10 were assigned. The change in the grading system is tabulated and compared separately.Results: Patients age ranged from 55-80 years. The number of cases were 3,12,15,19 and 11 categorized under grade group I, grade group II, grade group III, grade group IV, grade group V cancer respectively according to modified gleason grading.Conclusions: Modified Gleason is a simplified grading system which may reduce over treatment of indolent prostate cancer. New gleasons grading clarifies the clinicians about the dilemma of gleason scores, offering an excellent prognostic stratification of this carcinoma

Nearly Optimal Embeddings of Flat Tori

We show that for any n-dimensional lattice ? ? ??, the torus ??/? can be embedded into Hilbert space with O(?{nlog n}) distortion. This improves the previously best known upper bound of O(n?{log n}) shown by Haviv and Regev (APPROX 2010, J. Topol. Anal. 2013) and approaches the lower bound of ?(?n) due to Khot and Naor (FOCS 2005, Math. Ann. 2006)

ff-Policy Gradients: A General Framework for Goal Conditioned RL using ff-Divergences

Goal-Conditioned Reinforcement Learning (RL) problems often have access to sparse rewards where the agent receives a reward signal only when it has achieved the goal, making policy optimization a difficult problem. Several works augment this sparse reward with a learned dense reward function, but this can lead to sub-optimal policies if the reward is misaligned. Moreover, recent works have demonstrated that effective shaping rewards for a particular problem can depend on the underlying learning algorithm. This paper introduces a novel way to encourage exploration called $f$-Policy Gradients, or $f$-PG. $f$-PG minimizes the f-divergence between the agent's state visitation distribution and the goal, which we show can lead to an optimal policy. We derive gradients for various f-divergences to optimize this objective. Our learning paradigm provides dense learning signals for exploration in sparse reward settings. We further introduce an entropy-regularized policy optimization objective, that we call $state$-MaxEnt RL (or $s$-MaxEnt RL) as a special case of our objective. We show that several metric-based shaping rewards like L2 can be used with $s$-MaxEnt RL, providing a common ground to study such metric-based shaping rewards with efficient exploration. We find that $f$-PG has better performance compared to standard policy gradient methods on a challenging gridworld as well as the Point Maze and FetchReach environments. More information on our website https://agarwalsiddhant10.github.io/projects/fpg.html.Comment: Accepted at NeurIPS 202

Two new species of South Asian Cnemaspis Strauch, 1887 (Squamata: Gekkonidae) from the Gingee Hills, Tamil Nadu, India

Abstract We describe two new small-bodied, sympatric species of south Asian Cnemaspis belonging to the mysoriensis + adii clade from the Gingee Hills in Tamil Nadu, peninsular India. The two new species can be easily distinguished from the other eight described members of the mysoriensis + adii clade by their dorsal pholidosis, the configuration of femoral and precloacal pores in males, a number of meristic characters and subtle differences in colouration, beside 6.7–20.8 % uncorrected pairwise ND2 sequence divergence. The two species represent different ecomorphs, one a stouter, microhabitat generalist and the other a more slender, elongate rock specialist. The discovery of two new species from granite boulder habitats and Tropical Dry Evergreen Forests is indicative of the importance of these areas for biodiversity. It is likely that similar rocky habitats across southern peninsular India will harbour many more undescribed species

Photography-based taxonomy is inadequate, unnecessary, and potentially harmful for biological sciences

The question whether taxonomic descriptions naming new animal species without type specimen(s) deposited in collections should be accepted for publication by scientific journals and allowed by the Code has already been discussed in Zootaxa (Dubois & Nemésio 2007; Donegan 2008, 2009; Nemésio 2009a–b; Dubois 2009; Gentile & Snell 2009; Minelli 2009; Cianferoni & Bartolozzi 2016; Amorim et al. 2016). This question was again raised in a letter supported by 35 signatories published in the journal Nature (Pape et al. 2016) on 15 September 2016. On 25 September 2016, the following rebuttal (strictly limited to 300 words as per the editorial rules of Nature) was submitted to Nature, which on 18 October 2016 refused to publish it. As we think this problem is a very important one for zoological taxonomy, this text is published here exactly as submitted to Nature, followed by the list of the 493 taxonomists and collection-based researchers who signed it in the short time span from 20 September to 6 October 2016

A Report of Geckoella Nebulosa (Beddome, 1870) from Seoni District, Madhya Pradesh

Volume: 104Start Page: 222End Page: 22