Let P be a finite partially ordered set, briefly a finite poset. We will show that for any P -persistent object X in the category of finite topological spaces, there is a P− weighted graph, whose clique complex has the same P -persistent homology as X.

Paul M. Alsing∗1, Howard A. Blair†2, Matthew Corne‡1, Gordon Jones§3, Warner A. Miller¶4, Konstantin Mischaikow‖5 and Vidit Nanda∗∗6 Air Force Research Laboratory, Information Directorate, Rome, NY 13441 Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13244 Department of Computer Science, University of Michigan, Ann Arbor, MI 48109 Department of Phys...

A number of indicators and signals that lend themselves to monitoring by remote-sensing satellites provide a warning of land degradation. These include loss of vegetative cover, wind and water erosion, soil salinization, deterioration of the soil structure, drier soil, increased reflectance, higher land surface temperatures, and changes in land cover type. But because soil and vegetation change...

Patients with 'persistent vegetative state' (PVS) are often cited in the discussions of ethicists as examples of human beings who are unconscious and do not experience life, and a number of theoretical and practical recommendations have been made on that basis. This article examines the evidence and the theoretical rationale for the belief that people with PVS are unconscious and finds them wan...

The theory of persistent homology opens up the possibility to reason about topological features of a space or a function quantitatively and in combinatorial terms. We refer to this new angle at a classical subject within algebraic topology as a point calculus, which we present for the family of interlevel sets of a real-valued function. Our account of the subject is expository, devoid of proofs...

Computer role playing games, particularly those with persistent worlds, often allow players to buy and sell goods and services with computer controlled non-player characters (NPCs). The prices for these goods and services are often determined a priori, and remain fixed for the game’s duration. As a result, prices do not respond to changes in supply and demand, nor does supply and demand respond...

b) It was shown that the prepared derivatives distinctly put a stop to the postgerminal development of spores and the vegetative growth of Bacillus cereus 8. Chemical investigation, as well as biological testing of the prepared derivatives is continued. It can be assumed that the easy method of preparation described here will also be useful in the case of other basic peptides possessing antibio...

Rheumatoid arthritis is a painful inflammatory disorder. Patients seek relief mostly with analgesics and anti-inflammatory drugs which are rife with life-threatening side effects. Alterations in the body‘s potassium (K) status may be one such factor. K along with sodium is critical to cellular homeostasis and the electrophysiology of nerve impulses. This review is based on the premise that K ca...