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Graph Traversals as Universal Constructions [article]

Siddharth Bhaskar, Robin Kaarsgaard
2021 arXiv   pre-print
We exploit a decomposition of graph traversals to give a novel characterization of depth-first and breadth-first traversals as universal constructions. Specifically, we introduce functors from two different categories of edge-ordered directed graphs into two different categories of transitively closed edge-ordered graphs; one defines the lexicographic depth-first traversal and the other the lexicographic breadth-first traversal. We show that each functor factors as a composition of universal
more » ... structions, and that the usual presentation of traversals as linear orders on vertices can be recovered with the addition of an inclusion functor. Finally, we raise the question of to what extent we can recover search algorithms from the categorical description of the traversal they compute.
arXiv:2104.14877v1 fatcat:l3tkrmlfuzdvdnmn7pohiwjgqa

Algorithmic Traversals of Infinite Graphs [article]

Siddharth Bhaskar, Anton Jay Kienzle
2018 arXiv   pre-print
Finally, we are indebted to Haverford College and the Zweifler Family Fund for Student Researches in the Sciences for supporting the research project of Jay Kienzle with Siddharth Bhaskar during the summer  ... 
arXiv:1810.09974v1 fatcat:2enrz4nr3rd7pfyvh4dwr2t2s4

Thicket Density [article]

Siddharth Bhaskar
2020 arXiv   pre-print
We define a new type of "shatter function" for set systems that satisfies a Sauer-Shelah type dichotomy, but whose polynomial-growth case is governed by Shelah's 2-rank instead of VC dimension. We identify the rate of growth of this shatter function, the quantity analogous to VC density, with Shelah's ω-rank.
arXiv:1702.03956v4 fatcat:tzuhbj5sanff3nkjopr5oa4ysu

Traversal-invariant characterizations of logarithmic space [article]

Siddharth Bhaskar, Steven Lindell, Scott Weinstein
2020 arXiv   pre-print
We give a novel descriptive-complexity theoretic characterization of L and NL computable queries over finite structures using traversal invariance. We summarize this as (N)L = FO + (breadth-first) traversal-invariance.
arXiv:2006.07067v1 fatcat:eroaqig6qrf2tdoyut5xdfqeke

Asymptotic Logical Uncertainty and The Benford Test [article]

Scott Garrabrant, Siddharth Bhaskar, Abram Demski, Joanna Garrabrant, George Koleszarik, Evan Lloyd
2015 arXiv   pre-print
We give an algorithm A which assigns probabilities to logical sentences. For any simple infinite sequence of sentences whose truth-values appear indistinguishable from a biased coin that outputs "true" with probability p, we have that the sequence of probabilities that A assigns to these sentences converges to p.
arXiv:1510.03370v1 fatcat:xhe764bwurb2tcao4kslrao2ti

Computing Optimal Tolls in Routing Games without Knowing the Latency Functions [article]

Siddharth Barman, Umang Bhaskar, Chaitanya Swamy
2015 arXiv   pre-print
We consider the following question: in a nonatomic routing game, can the tolls that induce the minimum latency flow be computed without knowing the latency functions? Since the latency functions are unknown, we assume we are given an oracle that has access to the underlying routing game. A query to the oracle consists of tolls on edges, and the response is the resulting equilibrium flow. We show that in this model, it is impossible to obtain optimal tolls. However, if we augment the oracle so
more » ... at it returns the total latency of the equilibrium flow induced by the tolls in addition to the flow itself, then the required tolls can be computed with a polynomial number of queries.
arXiv:1505.04897v1 fatcat:u4b7dtilyzht7ikobzpgjgc6fu

Tight Approximation Algorithms for p-Mean Welfare Under Subadditive Valuations [article]

Siddharth Barman, Umang Bhaskar, Anand Krishna, Ranjani G. Sundaram
2020 arXiv   pre-print
Acknowledgements Siddharth Barman gratefully acknowledges the support of a Ramanujan Fellowship (SERB -SB/S2/RJN-128/2015) and a Pratiksha Trust Young Investigator Award.  ... 
arXiv:2005.07370v1 fatcat:mmvnsebpqff33alnppay35gqla

Fractionalization and the Municipal Bond Market

Daniel B. Bergstresser, Randolph B. Cohen, Siddharth Bhaskar Shenai
2011 Social Science Research Network  
We study the impact of ethnic and religious fractionalization on the U.S. municipal debt market, and find that issuers from more ethnically and religiously fractionalized counties pay higher yields on their municipal debt. A two standard deviation increase in religious fractionalization is associated with a six basis point increase in bond yields, and a two standard deviation increase in ethnic fractionalization is associated with a ten basis point increase. To provide a scale for these
more » ... a four-notch rating change, from AAA to AA-, is associated with an eight basis point increase in yields. Additional analysis suggests that at least some of this effect is not driven by the risk of the bonds, but instead reflects inefficiency in the underwriting process.
doi:10.2139/ssrn.1844685 fatcat:bqxtjmhyjzezrh4izujx5rjrjm

Financial Guarantors and the 2007-2009 Credit Crisis

Siddharth Bhaskar Shenai, Randolph B. Cohen, Daniel B. Bergstresser
2010 Social Science Research Network  
More than half of the municipal bonds issued between 1995 and 2009 were sold with bond insurance. During the credit crisis the perceived credit quality of the financial guarantors fell, and yields on insured bonds exceeded yields on equivalent uninsured issues. It does not appear that either property and casualty insurers or open-end municipal mutual funds were dumping insured bonds; analysis of holdings data indicates that their propensity to sell bonds was unusually low for the issues insured
more » ... by troubled insurers. At least on a bond-by-bond basis, the yield inversion phenomenon is also not explained by the rapid liquidation of Tender Option Bond (TOB) programs, which disproportionately held insured issues. Finally, during the recent crisis the insured bonds have become significantly less liquid than uninsured municipal debt.
doi:10.2139/ssrn.1571627 fatcat:pmggdea73rdknlnhwbtgraunn4

Asymptotic Logical Uncertainty and the Benford Test [chapter]

Scott Garrabrant, Tsvi Benson-Tilsen, Siddharth Bhaskar, Abram Demski, Joanna Garrabrant, George Koleszarik, Evan Lloyd
2016 Lecture Notes in Computer Science  
We give an algorithm AL,T which assigns probabilities to logical sentences. For any simple infinite sequence {φs n } of sentences whose truthvalues appear indistinguishable from a biased coin that outputs "true" with probability p, we have limn→∞ AL,T (sn) = p.
doi:10.1007/978-3-319-41649-6_20 fatcat:egz4zipozzceznb4kxyiojyugq

On the Existence of Low-Rank Explanations for Mixed Strategy Behavior [chapter]

Siddharth Barman, Umang Bhaskar, Federico Echenique, Adam Wierman
2014 Lecture Notes in Computer Science  
Nash equilibrium is used as a model to explain the observed behavior of players in strategic settings. For example, in many empirical applications we observe player behavior, and the problem is to determine if there exist payoffs for the players for which the equilibrium corresponds to observed player behavior. Computational complexity of Nash equilibria is an important consideration in this framework. If the instance of the model that explains observed player behavior requires players to have
more » ... olved a computationally hard problem, then the explanation provided is questionable. In this paper we provide conditions under which Nash equilibrium is a reasonable explanation for strategic behavior, i.e., conditions under which observed behavior of players can be explained by games in which Nash equilibria are easy to compute. We identify three structural conditions and show that if the data set of observed behavior satisfies any of these conditions, then it is consistent with payoff matrices for which the observed Nash equilibria could have been computed efficiently. Our conditions admit large and structurally complex data sets of observed behavior, showing that even with complexity considerations, Nash equilibrium is often a reasonable model.
doi:10.1007/978-3-319-13129-0_38 fatcat:psb3fxkc7vfehl7gzgzqtn2zui

Clinical significance of cysteine cathepsins in human dilated cardiomyopathy

Siddharth Mehra, Manish Kumar, Ratnakar Singh, Bhaskar Thakur, Rajiv Narang, Shyam S. Chauhan
2015 Indian Heart Journal  
doi:10.1016/j.ihj.2015.10.261 fatcat:mkkw7k6klrfjngw6fhz5ycgy7u

The empirical implications of rank in Bimatrix games

Siddharth Barman, Umang Bhaskar, Federico Echenique, Adam Wierman
2013 Proceedings of the fourteenth ACM conference on Electronic commerce - EC '13  
Bhaskar and A. Wierman, Computing and Mathematical Sciences, California Institute of Technology; F. Echenique, Division of the Humanities and Social Sciences, California Institute of Technology.  ... 
doi:10.1145/2492002.2482589 dblp:conf/sigecom/BarmanBEW13 fatcat:zdbrlak4kvblhcu4i6scslhkie

On the Existence of Low-Rank Explanations for Mixed Strategy Behavior [article]

Siddharth Barman, Umang Bhaskar, Federico Echenique, Adam Wierman
2014 arXiv   pre-print
Nash equilibrium is used as a model to explain the observed behavior of players in strategic settings. For example, in many empirical applications we observe player behavior, and the problem is to determine if there exist payoffs for the players for which the equilibrium corresponds to observed player behavior. Computational complexity of Nash equilibria is an important consideration in this framework. If the instance of the model that explains observed player behavior requires players to have
more » ... olved a computationally hard problem, then the explanation provided is questionable. In this paper we provide conditions under which Nash equilibrium is a reasonable explanation for strategic behavior, i.e., conditions under which observed behavior of players can be explained by games in which Nash equilibria are easy to compute. We identify three structural conditions and show that if the data set of observed behavior satisfies any of these conditions, then it is consistent with payoff matrices for which the observed Nash equilibria could have been computed efficiently. Our conditions admit large and structurally complex data sets of observed behavior, showing that even with complexity considerations, Nash equilibrium is often a reasonable model.
arXiv:1311.2655v2 fatcat:vyd7oy2vzbhbvi3zvkulbxsbqy

The empirical implications of rank in Bimatrix games

Siddharth Barman, Umang Bhaskar, Federico Echenique, Adam Wierman
2013 Proceedings of the fourteenth ACM conference on Electronic commerce  
doi:10.1145/2482540.2482589 fatcat:lflq6w5l7jdy7mbfspbibexqra
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