The Founding Fathers\u27 Shift Towards Anthropological Pessimism: From the Articles to the Constitution

American colonists grew to abhor the evils of a strong and tyrannical government. After freeing themselves, they created an intentionally weak government that placed trust in the masses to contribute to the country’s well-being. The weak government of the Articles of Confederation was too weak, and the people did not act as virtuously as was hoped. There were many problems of the Articles, and eventually a poor economy led to riots and rebellions. After being given nearly unbridled freedom, the people revealed themselves to be selfish. The Founding Fathers decided that the people needed a stronger government to regulate society but would not become tyrannical

Squaring The Circle In The Hyperbolic Disk

Bolyai ended his 1832 introduction to non-Euclidean geometry with a strategy for constructing regular quadrilaterals (squares) and circles of the same area. In this article, we provide the steps for these constructions in the Poincare disk. We come to the surprising conclusion that Bolyai\u27s strategy of building the circle and square separately is the only way to perform the constructions. That is, we cannot in general construct the square from the circle, nor vice versa

Long-Term Vegetation Response to Grazing on a Southwest Montana Foothills Range

Long-term vegetation data collected in area under known management provides an opportunity for understanding the potential implications of vegetation response to grazing management. Short-term studies (2-3 years) are unable to capture vegetation response due to the ecological inertia of the system and temporary fluctuations due to weather patterns. When Montana State University purchased Red Bluff Ranch in 1956, it was heavily stocked but the range was thought to be in acceptable condition. Stocking rates were lowered nonetheless. In 1958, 74 vegetation monitoring transects were established. In 2017 we attempted to relocate transects in two pastures currently used for winter grazing. Of the 28 transects in both pastures, we were able to relocate and read 11. Using original methodology, we collected basal cover data along five five-foot subplots randomly located around each transect. Data were analyzed using a paired Mann-Whitney U test. Cheatgrass (Bromus tectorum) exhibited the greatest change in cover, increasing from 0.4% in 1958 to 16.1% in 2017 (P < 0.01), and was present at 9 of the 11 monitoring sites. Perennial grass cover increased from 4.3% to 13.0% (P < 0.01). Litter cover increased from 49.2% to 58.4% (P < 0.05). Bare ground decreased from 35.2% to 3.0% (P < 0.01). The increase in cheatgrass cover explains a majority of the increase in litter and the extreme reduction in bare ground. The data indicate that the condition of the range may not have been as high as first thought, and, while cover of perennial species can increase under moderate stocking, rangeland may still be susceptible to invasion by cheatgrass. The invasion of cheatgrass may be attributable to the early spring flush of organic nitrogen associated with winter grazing

Energy-constrained two-way assisted private and quantum capacities of quantum channels

With the rapid growth of quantum technologies, knowing the fundamental characteristics of quantum systems and protocols is essential for their effective implementation. A particular communication setting that has received increased focus is related to quantum key distribution and distributed quantum computation. In this setting, a quantum channel connects a sender to a receiver, and their goal is to distill either a secret key or entanglement, along with the help of arbitrary local operations and classical communication (LOCC). In this work, we establish a general theory of energy-constrained, LOCC-assisted private and quantum capacities of quantum channels, which are the maximum rates at which an LOCC-assisted quantum channel can reliably establish secret key or entanglement, respectively, subject to an energy constraint on the channel input states. We prove that the energy-constrained squashed entanglement of a channel is an upper bound on these capacities. We also explicitly prove that a thermal state maximizes a relaxation of the squashed entanglement of all phase-insensitive, single-mode input bosonic Gaussian channels, generalizing results from prior work. After doing so, we prove that a variation of the method introduced in [Goodenough et al., New J. Phys. 18, 063005 (2016)] leads to improved upper bounds on the energy-constrained secret-key-agreement capacity of a bosonic thermal channel. We then consider a multipartite setting and prove that two known multipartite generalizations of the squashed entanglement are in fact equal. We finally show that the energy-constrained, multipartite squashed entanglement plays a role in bounding the energy-constrained LOCC-assisted private and quantum capacity regions of quantum broadcast channels.Comment: 31 pages, 6 figure

Entropic Bounds on Two-Way Assisted Secret-Key Agreement Capacities of Quantum Channels

In order to efficiently put quantum technologies into action, we must know the characteristics of the underlying quantum systems and effects. An interesting example is the use of the secret-key-agreement capacity of a quantum channel as a guide and measure for the implementation of quantum key distribution (QKD) and distributed quantum computation. We define the communication task of establishing a secret key over a quantum channel subject to an energy constraint on the input state and while allowing for unlimited local operations and classical communication (LOCC) between a sender and receiver. We then use the energy-constrained squashed entanglement to bound the capacity of the channel for secret-key agreement, and we show that a thermal state input maximizes a relaxation of this bound for phase-insensitive, single-mode Gaussian channels. We also establish improved upper bounds on the energy-constrained secret-key-agreement capacity for a bosonic thermal channel that is not entanglement breaking. We then generalize our results to the multipartite setting and show that the energy-constrained multipartite squashed entanglement bounds the LOCC-assisted private capacity region for a quantum broadcast channel. Next, we define the broadcast amplitude damping channel. In the setting of QKD, we discuss a communication task using the broadcast amplitude damping channel and give bounds on its achievable rate region

Squaring the Circle in Elliptic Geometry

Constructing a regular quadrilateral (square) and circle of equal area was proved impossible in Euclidean geometry in 1882. Hyperbolic geometry, however, allows this construction. In this article, we complete the story, providing and proving a construction for squaring the circle in elliptic geometry. We also find the same additional requirements as the hyperbolic case: only certain angle sizes work for the squares and only certain radius sizes work for the circles; and the square and circle constructions do not rely on each other