Omnibus Sequences, Coupon Collection, and Missing Word Counts

An {\it Omnibus Sequence} of length $n$ is one that has each possible "message" of length $k$ embedded in it as a subsequence. We study various properties of Omnibus Sequences in this paper, making connections, whenever possible, to the classical coupon collector problem.Comment: 26 page

Computing absorbing times via fluid approximations

In this paper, we compute the absorbing time Tn of a n-dimensional discrete time Markov chain made of n components, each with an absorbing state and evolving in mutual exclusion. We show that the random absorbing time Tn is well approximated by a deterministic time tn that is the first time when a fluid approximation of the chain approaches the absorbing state at a distance 1/n. We provide an asymptotic expansion of tn that uses the spectral decomposition of the kernel of the chain as well as the asymptotic distribution of Tn, relying on extreme values theory. We show the applicability of this approach with three different problems: the coupon collector, the erasure channel lifetime and the coupling times of random walks in high dimensional spaces

Algorithms for Jumbled Pattern Matching in Strings

The Parikh vector p(s) of a string s is defined as the vector of multiplicities of the characters. Parikh vector q occurs in s if s has a substring t with p(t)=q. We present two novel algorithms for searching for a query q in a text s. One solves the decision problem over a binary text in constant time, using a linear size index of the text. The second algorithm, for a general finite alphabet, finds all occurrences of a given Parikh vector q and has sub-linear expected time complexity; we present two variants, which both use a linear size index of the text.Comment: 18 pages, 9 figures; article accepted for publication in the International Journal of Foundations of Computer Scienc

Markov chains, R\mathscr R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on $\mathscr R$-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via M\"obius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.Comment: Dedicated to Stuart Margolis on the occasion of his sixtieth birthday; 71 pages; final version to appear in IJA

Victory Vol. 3, No. 23

These weekly publications from ca. December 1940 to 1944 fell under the titles of Defense and Victory. Defense was the “Official weekly bulletin of the Office of Emergency Management.” Victory was the “Official weekly bulletin of the Office of War Information.” The publications were designed to provide information to the civilian population on war related topics concentrating on economic issues. Established in May 20, 1941, the Office of Civilian Defense was created “to assure effective coordination of Federal relations with State and local governments engaged in furtherance of war programs; to provide for necessary cooperation with state and local governments with respect to measures for adequate protection of civilian population in war emergencies; and to facilitate participation by all persons in war programs.

Understanding the demand side of social protection programmes: the case of public distribution of food in India

India’s poor performance in reducing hunger and malnutrition, despite sustained economic growth, is considered “a national shame” (as stated by former Prime Minister of India, Manmohan Singh, 2012). Faced with this, successive governments have implemented large-scale food security and anti-poverty programmes. The Public Distribution System (PDS), the world’s largest food subsidy programme, has been the cornerstone of such initiatives. The National Food Security Act (NFSA) 2013, further broadens the scope of PDS by raising the level of subsidies, expanding coverage, and emphasising demand, especially in the choice of the food basket. Yet, PDS is plagued with charges of corruption, overpricing and delivery of low-quality grains. Additionally, significant power asymmetries are visible in the poor delivery of services, time-consuming bureaucratic procedures and ineffective grievance redressal systems. Though several possible reasons account for these problems, one factor that is generally overlooked is lack of compatibility between rights-holders’ need and what PDS is delivering. My thesis seeks to fill this research gap by investigating how PDS performs in meeting community’s needs and preferences (including their interests, opportunities and constraints). My objectives are three-fold: assessing the role of heterogeneity in determining access, level of satisfaction, and possible remedies in cases of entitlement snatching. Entitlement snatching refers to the acts of the PDS functionaries to not let the rights holders get the right price, quantity or quality as mandated by law. Drawing on Sen’s entitlement approach (1981), Ribot and Peluso’s (2003) theory of access, and interdisciplinary approaches from economics, sociology and psychology, I argue that heterogeneity drives what is needed, preferred or demanded from the PDS. Through mixed methods analysis, I explore in depth the role of social heterogeneity, in terms of class, caste, gender and political affiliation, in accessing the PDS. My research is also engaged in a comparative analysis across three Indian states of Bihar, Odisha and Eastern Uttar Pradesh, representing diversity in socio-economic conditions, cultural norms, governance systems, and political structures. The thesis demonstrates how power relations embedded in local politics, caste and class heterogeneity, and political economy mediate access through state transfers. I emphasize the centrality of demand in understanding the effectiveness of the system

Mental Commitment Cases of 1971 Supreme Court Term

Even in areas where legal representation has become available to the poor through the efforts of Legal Services programs, there is still one group that is almost universally denied representation: those confined under the various forms of civil commitment and patients in mental health institutions. Almost by definition in need of legal counsel and predictably indigent, they are faced with interpersonal and institutional barriers that further reduce their chances to obtain representation. It is the position of the National Health Law Program that Legal Services programs throughout the country should focus some of their attention towards this portion of their communities, to assess the need for legal services in the field of mental health and to develop a role in providing these services. This article is intended to stimulate an interest in the mental health field and to serve as an introduction to the related law