Counting subgraphs of coloring graphs

The chromatic polynomial $\pi_{G}(k)$ of a graph $G$ can be viewed as counting the number of vertices in a family of coloring graphs $\mathcal C_k(G)$ associated with (proper) $k$-colorings of $G$ as a function of the number of colors $k$. These coloring graphs can be understood as a reconfiguration system. We generalize the chromatic polynomial to $\pi_G^{(H)}(k)$, counting occurrences of arbitrary induced subgraphs $H$ in these coloring graphs, and we prove that these functions are polynomial in $k$. In particular, we study the chromatic pairs polynomial $\pi_{G}^{(P_2)}(k)$, which counts the number of edges in coloring graphs, corresponding to the number of pairs of colorings that differ on a single vertex. We show two trees share a chromatic pairs polynomial if and only if they have the same degree sequence, and we conjecture that the chromatic pairs polynomial refines the chromatic polynomial in general. We also instantiate our polynomials with other choices of $H$ to generate new graph invariants.Comment: 25 pages, 14 figure

How to Share a Lattice Trapdoor: Threshold Protocols for Signatures and (H)IBE

We develop secure \emph{threshold} protocols for two important operations in lattice cryptography, namely, generating a hard lattice $\Lambda$ together with a ``strong\u27\u27 trapdoor, and sampling from a discrete Gaussian distribution over a desired coset of $\Lambda$ using the trapdoor. These are the central operations of many cryptographic schemes: for example, they are exactly the key-generation and signing operations (respectively) for the GPV signature scheme, and they are the public parameter generation and private key extraction operations (respectively) for the GPV IBE. We also provide a protocol for trapdoor delegation, which is used in lattice-based hierarchical IBE schemes. Our work therefore directly transfers all these systems to the threshold setting. Our protocols provide information-theoretic (i.e., statistical) security against adaptive corruptions in the UC framework, and they are private and robust against an optimal number of semi-honest or malicious parties. Our Gaussian sampling protocol is both noninteractive and efficient, assuming either a trusted setup phase (e.g., performed as part of key generation) or a sufficient amount of interactive but offline precomputation, which can be performed before the inputs to the sampling phase are known

Environmental effects on water intake and water intake prediction in growing beef cattle

Water is an essential nutrient, but there are few recent studies that evaluate how much water individual beef cattle consume and how environmental factors affect an individual’s water intake (WI). Most studies have focused on WI of whole pens rather than WI of individual animals. Thus, the objective of this study was to evaluate the impact of environmental parameters on individual-animal WI across different seasons and develop prediction equations to estimate WI, including within different environments and management protocols. Individual daily feed intake and WI records were collected on 579 crossbred steers for a 70-d period following a 21-d acclimation period for feed and water bunk training. Steers were fed in 5 separate groups over a 3-yr period from May 2014 to March 2017. Individual weights were collected every 14 d and weather data were retrieved from the Oklahoma Mesonet’s Stillwater station. Differences in WI as a percent of body weight (WI%) were analyzed accounting for average temperature (TAVG), relative humidity (HAVG), solar radiation (SRAD), and wind speed (WSPD). Seasonal (summer vs. winter) and management differences (ad libitum vs. slick bunk) were examined. Regression analysis was utilized to generate 5 WI prediction equations (overall, summer, winter, slick, and ad libitum). There were significant (P \u3c 0.05) differences in WI between all groups when no environmental parameters were included in the model. Although performance was more similar after accounting for all differences in weather variables, significant (P \u3c 0.05) seasonal and feed management differences were still observed for WI%, but were less than 0.75% of steer body weight. The best linear predictors of daily WI (DWI) were dry mater intake (DMI), metabolic body weights (MWTS), TAVG, SRAD, HAVG, and WSPD. Slight differences in the coefficient of determinations for the various models were observed for the summer (0.34), winter (0.39), ad libitum (0.385), slick bunk (0.41), and overall models (0.40). Based on the moderate R2 values for the WI prediction equations, individual DWI can be predicted with reasonable accuracy based on the environmental conditions that are present, MWTS, and DMI consumed, but substantial variation exists in individual animal WI that is not accounted for by these models

The \u27Healthy Parks-Healthy People\u27 Movement in Canada: Progress, Challenges, and an Emerging Knowledge and Action Agenda

In this article, we outline progress and challenges in establishing effective health promotion tied to visitor experiences provided by protected and conserved areas in Canada. Despite an expanding global evidence base, case studies focused on aspects of health and well-being within Canada’s protected and conserved areas remain limited. Data pertaining to motivations, barriers and experiences of visitors are often not collected by governing agencies and, if collected, are not made generally available or reported on. There is an obvious, large gap in research and action focused on the needs and rights of groups facing systemic barriers related to a variety of issues including, but not limited to, access, nature experiences, and needs with respect to health and well-being outcomes. Activation of programmes at the site level continue to grow, and Park Prescription programmes, as well as changes to the Accessible Canada Act, represent significant, positive examples of recent cross-sector policy integration. Evaluations of outcomes associated with HPHP programmes have not yet occurred but will be important to adapting interventions and informing cross-sector capacity building. We conclude by providing an overview of gaps in evidence and practice that, if addressed, can lead to more effective human health promotion vis-à-vis nature contact in protected and conserved areas in Canada