Linkages Between the Phenologies of Jack Pine \u3ci\u3e(Pinus Banksiana)\u3c/i\u3e Foliage and Jack Pine Budworm (Lepidoptera: Tortricidae)

A field study conducted in 2001 and 2002 in the Michigan Upper Peninsula investigated seasonal associations between the development of jack pine, Pinus banksiana Lamb., and larvae of the jack pine budworm Choristoneura pinus Freeman (Lepidoptera: Tortricidae). There was almost no active relationship between post-diapause emerging second instars and elongation of vegetative shoots. Early instars were not closely synchronized with the flushing of current-year needle fascicles, which is required to optimize larval feeding. How- ever, there were close feeding and shelter relationships between early instars and year-2 pollen cone development. Associations with, and larval damage to, year-2 seed cones were dependent upon larval population size and posed only minimal and periodic threats to jack pine seed production. As a consequence, early instar jack pine budworm relied almost exclusively on pollen cones for survival. Third to fifth instars vacated pollen cones as soon as they became desiccated. Only then did these larvae start close associations with vegetative shoots. First, they excised partially emerged needles at their base, and when the needle-pairs completely escaped their fascicle sheath, the larvae fed routinely on the complete needle lamina. Late instars, pupae and adults were associated with previous years’ and current-year foliage without any apparent bias. This study has shown that it might be more practical to time insecticide strategies, which are intended to manage jack pine budworm larvae, to the tree’s phenology rather than jack pine budworm larval indices

A Fascinating Polynomial Sequence arising from an Electrostatics Problem on the Sphere

A positive unit point charge approaching from infinity a perfectly spherical isolated conductor carrying a total charge of +1 will eventually cause a negatively charged spherical cap to appear. The determination of the smallest distance $\rho(d)$ ($d$ is the dimension of the unit sphere) from the point charge to the sphere where still all of the sphere is positively charged is known as Gonchar's problem. Using classical potential theory for the harmonic case, we show that $1+\rho(d)$ is equal to the largest positive zero of a certain sequence of monic polynomials of degree $2d-1$ with integer coefficients which we call Gonchar polynomials. Rather surprisingly, $\rho(2)$ is the Golden ratio and $\rho(4)$ the lesser known Plastic number. But Gonchar polynomials have other interesting properties. We discuss their factorizations, investigate their zeros and present some challenging conjectures.Comment: 12 pages, 6 figures, 1 tabl

Synthesis and evaluation of designed PKC modulators for enhanced cancer immunotherapy.

Bryostatin 1 is a marine natural product under investigation for HIV/AIDS eradication, the treatment of neurological disorders, and enhanced CAR T/NK cell immunotherapy. Despite its promising activity, bryostatin 1 is neither evolved nor optimized for the treatment of human disease. Here we report the design, synthesis, and biological evaluation of several close-in analogs of bryostatin 1. Using a function-oriented synthesis approach, we synthesize a series of bryostatin analogs designed to maintain affinity for bryostatin's target protein kinase C (PKC) while enabling exploration of their divergent biological functions. Our late-stage diversification strategy provides efficient access to a library of bryostatin analogs, which per our design retain affinity for PKC but exhibit variable PKC translocation kinetics. We further demonstrate that select analogs potently increase cell surface expression of CD22, a promising CAR T cell target for the treatment of leukemias, highlighting the clinical potential of bryostatin analogs for enhancing targeted immunotherapies

Unusual metallic phase in a chain of strongly interacting particles

We consider a one-dimensional lattice model with the nearest-neighbor interaction $V_1$ and the next-nearest neighbor interaction $V_2$ with filling factor 1/2 at zero temperature. The particles are assumed to be spinless fermions or hard-core bosons. Using very simple assumptions we are able to predict the basic structure of the insulator-metal phase diagram for this model. Computations of the flux sensitivity support the main features of the proposed diagram and show that the system maintains metallic properties at arbitrarily large values of $V_1$ and $V_2$ along the line $V_1-2V_2=\gamma J$, where $J$ is the hopping amplitude, and $\gamma\approx1.2$. We think that close to this line the system is a ``weak'' metal in a sense that the flux sensitivity decreases with the size of the system not exponentially but as $1/L^\alpha$ with $\alpha>1$.Comment: To appear in J. Phys. C; 9 revtex preprint pages + 4 ps figures, uuencode

Picture-Hanging Puzzles

We show how to hang a picture by wrapping rope around n nails, making a polynomial number of twists, such that the picture falls whenever any k out of the n nails get removed, and the picture remains hanging when fewer than k nails get removed. This construction makes for some fun mathematical magic performances. More generally, we characterize the possible Boolean functions characterizing when the picture falls in terms of which nails get removed as all monotone Boolean functions. This construction requires an exponential number of twists in the worst case, but exponential complexity is almost always necessary for general functions.Comment: 18 pages, 8 figures, 11 puzzles. Journal version of FUN 2012 pape

Popularity-Driven Networking

We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional to the degrees of the two nodes. Interestingly, this network exhibits two abrupt transitions, both occurring at finite times. The first is a percolation transition in which a giant component, containing a finite fraction of all nodes, is born. The second is a condensation transition in which the entire system condenses into a single, fully connected, component. We derive the size distribution of connected components as well as the degree distribution, which is purely exponential throughout the evolution. Furthermore, we present a criterion for the emergence of sudden condensation for general homogeneous connection rates.Comment: 5 pages, 2 figure

Analytic approach to stochastic cellular automata: exponential and inverse power distributions out of Random Domino Automaton

Inspired by extremely simplified view of the earthquakes we propose the stochastic domino cellular automaton model exhibiting avalanches. From elementary combinatorial arguments we derive a set of nonlinear equations describing the automaton. Exact relations between the average parameters of the model are presented. Depending on imposed triggering, the model reproduces both exponential and inverse power statistics of clusters.Comment: improved, new material added; 9 pages, 3 figures, 2 table

Universality in Uncertainty Relations for a Quantum Particle

A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is bounded from below. Whenever a global minimum exists, an uncertainty relation has been obtained. The squeezed number states of a harmonic oscillator are found to be universal: no other pure or mixed states will saturate any such relation. Geometrically, we identify a convex uncertainty region in the space of second moments which is bounded by the inequality derived by Robertson and Schrödinger. Our approach provides a unified perspective on existing uncertainty relations for a single continuous variable, and it leads to new inequalities for second moments which can be checked experimentally

Admission and Discharge Practices Among Assisted Living Communities: the Role of State Regulations and Organizational Characteristics

A better understanding of factors associated with assisted living admission and discharge practices can help identify communities that are more likely to allow residents to age in place. This study examined how state regulations and assisted living organizational characteristics relate to community admission and discharge practices for bathing, getting out of bed, and feeding

The maximally entangled symmetric state in terms of the geometric measure

The geometric measure of entanglement is investigated for permutation symmetric pure states of multipartite qubit systems, in particular the question of maximum entanglement. This is done with the help of the Majorana representation, which maps an n qubit symmetric state to n points on the unit sphere. It is shown how symmetries of the point distribution can be exploited to simplify the calculation of entanglement and also help find the maximally entangled symmetric state. Using a combination of analytical and numerical results, the most entangled symmetric states for up to 12 qubits are explored and discussed. The optimization problem on the sphere presented here is then compared with two classical optimization problems on the S^2 sphere, namely Toth's problem and Thomson's problem, and it is observed that, in general, they are different problems.Comment: 18 pages, 15 figures, small corrections and additions to contents and reference