Fred S. Roberts

Bio: Fred S. Roberts is an academic researcher from Rutgers University. The author has contributed to research in topics: Axiom & Chordal graph. The author has an hindex of 32, co-authored 181 publications receiving 5286 citations. Previous affiliations of Fred S. Roberts include Pennsylvania State University & Center for Discrete Mathematics and Theoretical Computer Science.

Measurement theory with applications to decisionmaking, utility, and the social sciences

Abstract: Introduction 1. Relations 2. Fundamental Measurement, Derived Measurement, and the Uniqueness Problem 3. Three Representation Problems: Ordinal, Extensive, and Difference Measurement 4. Applications to Psychophysical Scaling 5. Project Structures 6. Nontransitive Indifference, Probabilistic Consistency, and Measurement without Numbers 7. Decisionmaking under Risk or Uncertainty 8. Subjective Probability.

Applied Combinatorics

Abstract: Section 13.1 . 1(a). Add edges in the order {b, e}, {d, e}, {a, e}, {c, d}; 1(b). Add edges in the order {a, b}, {b, c}, {d, e}, {e, f}, {g, h}, {h, i}, {a, d}, {d, g}; 1(c). Add edges in the order {c, g}, {a, b}, {a, d}, {f, g}, {d, f}, {e, f} where ties were broken arbitrarily; 2(a). add edges {a, e}, {b, e}, {d, e}, {c, d}; 2(b). Add edges in the order {a, b}, {b, c}, {a, d}, {d, e}, {e, f}, {d, g}, {g, h}, {h, i}; 2(c). Add edges in the order {a, b}, {a, d}, {d, f}, {f, g}, {c, g}, {e, f}; 3(a). terminate with message disconnected; T ends up with 5 edges; 3(b). terminate with message disconnected; T ends up with 7 edges; 3(c). terminate with message disconnected; T ends up with 6 edges; 5. vat pairs: {7, 8}, {6, 7}, {1, 5}, {4, 5}, {5, 8}, {2, 3}, {3, 8}; 6. component pairs: {1, 4}, {2, 6}, {3, 4}, {1, 6}, {5, 6}; 9. (a): edges {b, c}, {c, e}, {c, d}, {a, b}; (b): edges {f, i}, {e, h}, {d, g}, {c, f}, {b, e}, {a, d}, {g, h}, {h, i}; (c): edges {d, e}, {c, d}, {a, e}, {b, c}, {e, f}, {d, g}; 11. yes; 12(a). edges {a, e}, {a, b}, {c, d}, {d, e}; 12(b). edges {c, e}, {a, b}, {c, d}, {b, d}; 13. in Step 1 of Kruskal’s Algorithm, set T = { the set of edges specified as having to belong to the spanning tree }; 16(a). for network (c): G′ has edges {a, b}, {c, g}, {a, d}, {f, g}, {d, f}; in the next iteration we add {e, f} and obtain a minimum spanning tree.

Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems.

Abstract: No calculus needed but strong finite math background required. Less of the usual CS orientation.

Machine learning

Abstract: Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Counting and Multidimensional Poverty Measurement

Abstract: This paper proposes a new methodology for multidimensional poverty measurement consisting of an identification method ρk that extends the traditional intersection and union approaches, and a class of poverty measures Mα. Our identification step employs two forms of cutoff: one within each dimension to determine whether a person is deprived in that dimension, and a second across dimensions that identifies the poor by ‘counting’ the dimensions in which a person is deprived. The aggregation step employs the FGT measures, appropriately adjusted to account for multidimensionality. The axioms are presented as joint restrictions on identification and the measures, and the methodology satisfies a range of desirable properties including decomposability. The identification method is particularly well suited for use with ordinal data, as is the first of our measures, the adjusted headcount ratio. We present some dominance results and an interpretation of the adjusted headcount ratio as a measure of unfreedom. Examples from the US and Indonesia illustrate our methodology.

Digraphs Theory Algorithms And Applications

Abstract: The theory of directed graphs has developed enormously over recent decades, yet this book (first published in 2000) remains the only book to cover more than a small fraction of the results. New research in the field has made a second edition a necessity. Substantially revised, reorganised and updated, the book now comprises eighteen chapters, carefully arranged in a straightforward and logical manner, with many new results and open problems. As well as covering the theoretical aspects of the subject, with detailed proofs of many important results, the authors present a number of algorithms, and whole chapters are devoted to topics such as branchings, feedback arc and vertex sets, connectivity augmentations, sparse subdigraphs with prescribed connectivity, and also packing, covering and decompositions of digraphs. Throughout the book, there is a strong focus on applications which include quantum mechanics, bioinformatics, embedded computing, and the travelling salesman problem. Detailed indices and topic-oriented chapters ease navigation, and more than 650 exercises, 170 figures and 150 open problems are included to help immerse the reader in all aspects of the subject. Digraphs is an essential, comprehensive reference for undergraduate and graduate students, and researchers in mathematics, operations research and computer science. It will also prove invaluable to specialists in related areas, such as meteorology, physics and computational biology.

Fuzzy Preference Modelling and Multicriteria Decision Support

Abstract: Introduction. 1. Fuzzy logical connectives. 2. Valued binary relations. 3. Valued preference modelling. 4. Similarity relations and valued orders. 5. Aggregation operations. 6. Ranking procedures. 7. Multiple criteria decision making. 8. Summary, perspectives and open problems. Index.

NeighborNet: An Agglomerative Method for the Construction of Planar Phylogenetic Networks

Abstract: We introduce NeighborNet, a network construction and data representation method that combines aspects of the neighbor joining (NJ) and SplitsTree. Like NJ, NeighborNet uses agglomeration: taxa are combined into progressively larger and larger overlapping clusters. Like SPLITSTREE, NeighborNet constructs networks rather than trees, and so can be used to represent multiple phylogenetic hypotheses simultaneously, or to detect complex evolutionary processes like recombination, lateral transfer and hybridization. NeighborNet tends to produce networks that are substantially more resolved than those made with SPLITSTREE. The method is efficient (O(n3) time) and is well suited for the preliminary analyses of complex phylogenetic data. We report results of three case studies: one based on mitochondrial gene order data from early branching eukaryotes, another based on nuclear sequence data from New Zealand alpine buttercups (Ranunculi), and a third on poorly corrected synthetic data.