A Bayesian Analogue of Gleason's Theorem

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.Comment: 14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published versio

Topological Test Spaces

A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with incommensurable random quantities. In the case of quantum mechanics, the relevant test space, the set of orthonormal bases of a Hilbert space, carries significant topological structure. This paper inaugurates a general study of topological test spaces. Among other things, we show that any topological test space with a compact space of outcomes is of finite rank. We also generalize results of Meyer and Clifton-Kent by showing that, under very weak assumptions, any second-countable topological test space contains a dense semi-classical test space.Comment: 12 pp., LaTeX 2e. To appear in Int. J. Theor. Phy

Aging in Falmouth: Assessing current and future needs of our aging population

This report describes the collaborative efforts undertaken by the Town of Falmouth Council on Aging Senior Center and the Center for Social and Demographic Research on Aging, within the McCormack Graduate School at the University of Massachusetts Boston. Beginning in Spring 2013, these organizations joined to conduct a needs assessment to investigate the needs, interests, preferences and opinions of the Town’s older resident population, with respect to aging in Falmouth. The focus of this report is on two cohorts of Falmouth residents—those aged 45 to 59 (referred to as “Boomers”), and the cohort of individuals who are currently aged 60 and over (“Seniors”)

Non-Contextual Hidden Variables and Physical Measurements

For a hidden variable theory to be indistinguishable from quantum theory for finite precision measurements, it is enough that its predictions agree for some measurement within the range of precision. Meyer has recently pointed out that the Kochen-Specker theorem, which demonstrates the impossibility of a deterministic hidden variable description of ideal spin measurements on a spin 1 particle, can thus be effectively nullified if only finite precision measurements are considered. We generalise this result: it is possible to ascribe consistent outcomes to a dense subset of the set of projection valued measurements, or to a dense subset of the set of positive operator valued measurements, on any finite dimensional system. Hence no Kochen-Specker like contradiction can rule out hidden variable theories indistinguishable from quantum theory by finite precision measurements in either class.Comment: Typo corrected. Final version: to appear in Phys. Rev. Let

Kochen-Specker theorem for a single qubit using positive operator-valued measures

A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure

The auxiliary use of LANDSAT data in estimating crop acreages: Results of the 1975 Illinois crop-acreage experiment

The author has identified the following significant results. It was found that classifier performance was influenced by a number of temporal, methodological, and geographical factors. Best results were obtained when corn was tasselled and near the dough stage of development. Dates earlier or later in the growing season produced poor results. Atmospheric effects on results cannot be independently measured or completely separated from the effects due to the maturity stage of the crops. Poor classifier performance was observed in areas where considerable spectral confusion was present

Classical Lie algebras and Drinfeld doubles

The Drinfeld double structure underlying the Cartan series An, Bn, Cn, Dn of simple Lie algebras is discussed. This structure is determined by two disjoint solvable subalgebras matched by a pairing. For the two nilpotent positive and negative root subalgebras the pairing is natural and in the Cartan subalgebra is defined with the help of a central extension of the algebra. A new completely determined basis is found from the compatibility conditions in the double and a different perspective for quantization is presented. Other related Drinfeld doubles on C are also considered.Comment: 11 pages. submitted for publication to J. Physics

Maximally Causal Quantum Mechanics

We present a new causal quantum mechanics in one and two dimensions developed recently at TIFR by this author and V. Singh. In this theory both position and momentum for a system point have Hamiltonian evolution in such a way that the ensemble of system points leads to position and momentum probability densities agreeing exactly with ordinary quantum mechanics.Comment: 7 pages,latex,no figures,to appear in Praman

Structural contributions to the pressure-tuned charge-density-wave to superconductor transition in ZrTe3: Raman scattering studies

Superconductivity evolves as functions of pressure or doping from charge-ordered phases in a variety of strongly correlated systems, suggesting that there may be universal characteristics associated with the competition between superconductivity and charge order in these materials. We present an inelastic light (Raman) scattering study of the structural changes that precede the pressure-tuned charge-density-wave (CDW) to superconductor transition in one such system, ZrTe3. In certain phonon bands, we observe dramatic linewidth reductions that accompany CDW formation, indicating that these phonons couple strongly to the electronic degrees of freedom associated with the CDW. The same phonon bands, which represent internal vibrations of ZrTe3 prismatic chains, are suppressed at pressures above ~10 kbar, indicating a loss of long-range order within the chains, specifically amongst intrachain Zr-Te bonds. These results suggest a distinct structural mechanism for the observed pressure-induced suppression of CDW formation and provide insights into the origin of pressure-induced superconductivity in ZrTe3.Comment: 6 pages, 5 figure

Aging in Boston: Preparing today for a growing tomorrow

Boston’s population is becoming older than ever before. The oldest Baby Boomer is approaching 70 and reinventing what it means to be a “senior citizen.” Waves of Boomers will forge a new path into later life, creating a population of seniors that is larger and more long-lived than previous cohorts, and diverse in new ways. In 2010, more than 14% of Boston’s residents were 60 years or older, representing 88,000 older people. By 2030, projected increases in the older population will result in as many as 130,000 seniors residing in Boston. How will Boston accommodate its growing older population? What steps may promote livability for Boston residents of all ages; where residents will want to, and can expect to, age in place with security, dignity, and well-being