Balakrishnan, K.

Consensus strategies for signed profiles on graphs (Article)

2012-06-15T00:00:00Z

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from <+,-> Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes.

Consensus strategies for signed profiles on graphs (Article)

2012-06-15T00:00:00Z

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from (+,-). Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes.

Consensus Strategies for Signed Profiles on Graphs (Research Paper)

2011-10-17T00:00:00Z

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from {+,-}. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes.

Axiomatic Characterization of the Antimedian Function on Paths and Hypercubes (Research Paper)

2011-03-04T00:00:00Z

An antimedian of a profile $\\pi = (x_1, x_2, \\ldots , x_k)$ of vertices of a graph $G$ is a vertex maximizing the sum of the distances to the elements of the profile. The antimedian function is defined on the set of all profiles on $G$ and has as output the set of antimedians of a profile. It is a typical location function for finding a location for an obnoxious facility. The `converse' of the antimedian function is the median function, where the distance sum is minimized. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper such a characterization is obtained for the two classes of graphs on which the antimedian is well-behaved: paths and hypercubes.

Rad21-cohesin haploinsufficiency impedes DNA repair and enhances gastrointestinal radiosensitivity in mice (Article)

2010-10-19T00:00:00Z

Approximately half of cancer-affected patients receive radiotherapy (RT). The doses delivered have been determined upon empirical experience based upon average radiation responses. Ideally higher curative radiation doses might be employed in patients with genuinely normal radiation responses and importantly radiation hypersensitive patients would be spared the consequences of excessive tissue damage if they were indentified before treatment. Rad21 is an integral subunit of the cohesin complex, which regulates chromosome segregation and DNA damage responses in eukaryotes. We show here, by targeted inactivation of this key cohesin component in mice, that Rad21 is a DNA-damage response gene that markedly affects animal and cell survival. Biallelic deletion of Rad21 results in early embryonic death. Rad21 heterozygous mutant cells are defective in homologous recombination (HR)-mediated gene targeting and sister chromatid exchanges. Rad21+/2animals exhibited sensitivity considerably greater than control littermates when challenged with whole body irradiation (WBI). Importantly, Rad21+/2animals are significantly more sensitive to WBI than Atm heterozygous mutant mice. Since supralethal WBI of mammals most typically leads to death via damage to the gastrointestinal tract (GIT) or the haematopoietic system, we determined the functional status of these organs in the irradiated animals. We found evidence for GIT hypersensitivity of the Rad21 mutants and impaired bone marrow stem cell clonogenic regeneration. These data indicate that Rad21 gene dosage is critical for the ionising radiation (IR) response. Rad21 mutant mice thus represent a new mammalian model for understanding the molecular basis of irradiation effects on normal tissues and have important implications in the understanding of acute radiation toxicity in normal tissues.

Median computation in graphs using consensus strategies (Research Paper)

2007-10-01T00:00:00Z

Following the Majority Strategy in graphs, other consensus strategies, namely Plurality Strategy, Hill Climbing and Steepest Ascent Hill Climbing strategies on graphs are discussed as methods for the computation of median sets of profiles. A review of algorithms for median computation on median graphs is discussed and their time complexities are compared. Implementation of the consensus strategies on median computation in arbitrary graphs is discussed.

The plurality strategy on graphs (Research Paper)

2006-09-15T00:00:00Z

The Majority Strategy for finding medians of a set of clients on a graph can be relaxed in the following way: if we are at v, then we move to a neighbor w if there are at least as many clients closer to w than to v (thus ignoring the clients at equal distance from v and w). The graphs on which this Plurality Strategy always finds the set of all medians are precisely those for which the set of medians induces always a connected subgraph.