We study k-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integer k = 1, 2, . . .. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, for k > 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is ne...

We study k-divisible partition structures, which are families of random set partitions whose block sizes are divisible by an integer k = 1, 2, . . .. In this setting, exchangeability corresponds to the usual invariance under relabeling by arbitrary permutations; however, for k > 1, the ordinary deletion maps on partitions no longer preserve divisibility, and so a random deletion procedure is ne...

Potassium (K) is essential for plant growth and vital soil health. However, despite high crop demand, K fertilization continues to be ignored or severely inadequate in Indian agriculture. Over time, this could lead severe depletion of reserve, irreversibly alter K-bearing minerals, adversely affect fertility productivity. Hence, we should comprehensively assess the alarming situation mining Ind...

We consider team optimal control of decentralized systems with linear dynamics, quadratic costs, and arbitrary disturbance that consist of multiple sub-populations with exchangeable agents (i.e., exchanging two agents within the same sub-population does not affect the dynamics or the cost). Such a system is equivalent to one where the dynamics and costs are coupled across agents through the mea...

A random partition of the positive integers is called partially exchangeable if for each finite sequence of positive integers n,, ... , nk, the probability that the partition breaks the first n1 + + nk integers into k particular classes, of sizes nl,.. . ., nk in order of their first elements, has the same value p(nl,...,nk) for every possible choice of classes subject to the sizes constraint. ...

BACKGROUND Hypervolemic hypernatremia is caused by an increase in total exchangeable Na(+) and K(+) in excess of an increment in total body H(2)O (TBW). Unlike patients with hypovolemic or euvolemic hypernatremia, treatment needs to be targeted at correcting not only the elevated plasma Na(+) concentration, but also there is an additional requirement to achieve negative H(2)O balance to correct...

A 500-MHz ‘H-NMR study on a double-stranded non-self-complementary DNA undecamer comprising a portion of the specific target site for the cyclic AMP receptor protein in thegal operon is presented. Using pre-steadystate nuclear Overhauser effect (NOE) measurements, all exchangeable imino, non-exchangeable base, methyl, and HI’, H2’ and H2” sugar proton resonances are assigned in a sequential man...

The conventional crop production practices including intensive tillage and open field residue burning in world’ largest rice-wheat system (RWS) are adversely affecting productivity besides deteriorating natural resources ecosystems’ sustainability. In order to improve productivity, potassium (K) use efficiency apparent K balance, adoption of conservation a RWS with management is considered high...