Arithmetic properties of eigenvalues of generalized Harper operators on graphs

Let \Qbar denote the field of complex algebraic numbers. A discrete group $G$ is said to have the $\sigma$-multiplier algebraic eigenvalue property, if for every matrix $A$ with entries in the twisted group ring over the complex algebraic numbers M_d(\Qbar(G,\sigma)), regarded as an operator on $l^2(G)^d$, the eigenvalues of $A$ are algebraic numbers, where $\sigma$ is an algebraic multiplier. Such operators include the Harper operator and the discrete magnetic Laplacian that occur in solid state physics. We prove that any finitely generated amenable, free or surface group has this property for any algebraic multiplier $\sigma$. In the special case when $\sigma$ is rational ($\sigma^n$=1 for some positive integer $n$) this property holds for a larger class of groups, containing free groups and amenable groups, and closed under taking directed unions and extensions with amenable quotients. Included in the paper are proofs of other spectral properties of such operators.Comment: 28 pages, latex2e, paper revise

Calibration Scheme for Large Kinetic Inductance Detector Arrays Based on Readout Frequency Response

Microwave kinetic inductance detector (MKID) provides a way to build large ground based sub-mm instruments such as NIKA and A-MKID. For such instruments, therefore, it is important to understand and characterize the response to ensure good linearity and calibration over wide dynamic range. We propose to use the MKID readout frequency response to determine the MKID responsivity to an input optical source power. A signal can be measured in a KID as a change in the phase of the readout signal with respect to the KID resonant circle. Fundamentally, this phase change is due to a shift in the KID resonance frequency, in turn due to a radiation induced change in the quasiparticle number in the superconducting resonator. We show that shift in resonant frequency can be determined from the phase shift by using KID phase versus frequency dependence using a previously measured resonant frequency. Working in this calculated resonant frequency, we gain near linearity and constant calibration to a constant optical signal applied in a wide range of operating points on the resonance and readout powers. This calibration method has three particular advantages: first, it is fast enough to be used to calibrate large arrays, with pixel counts in the thousand of pixels; second, it is based on data that are already necessary to determine KID positions; third, it can be done without applying any optical source in front of the array.Comment: Accepted to Journal of Low Temperature Physics LTD16 Special Issue, Low Temperature Detector 16 Conference Proceedings,manuscript number: #JLTP-D-15-00356R1, 6 pages, 5 figure

Revisiting the Problem of Searching on a Line

We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ratio achievable by any search strategy in the worst case. We present the first tight bounds on the exact optimal competitive ratio achievable, parameterized in terms of the given bounds on D, along with an optimal search strategy that achieves this competitive ratio. We prove that this optimal strategy is unique. We characterize the conditions under which an optimal strategy can be computed exactly and, when it cannot, we explain how numerical methods can be used efficiently. In addition, we answer several related open questions, including the maximal reach problem, and we discuss how to generalize these results to m rays, for any m >= 2

Four Years of Airborne Measurements of Wildfire Emissions in California, with a Focus on the Evolution of Emissions During the Soberanes Megafire

Biomass burning is an important source of trace gases and particles which can influence air quality on local, regional, and global scales. With wildfire events increasing due to changes in land use, increasing population, and climate change, characterizing wildfire emissions and their evolution is vital. In this work we report in situ airborne measurements of carbon dioxide (CO2), methane (CH4), water vapor (H2O), ozone (O3), and formaldehyde (HCHO) from nine wildfire events in California between 2013 and 2016, which were sampled as part of the Alpha Jet Atmospheric eXperiment (AJAX) based at NASA Ames Research Center. One of those fires, the Soberanes Megafire, began on 22 July 2016 and burned for three months. During that time, five flights were executed to sample emissions near and downwind of the Soberanes wildfire. In situ data are used to determine enhancement ratios (ERs), or excess mixing ratio relative to CO2, as well as assess O3 production from the fire. Changes in the emissions as a function of fire evolution are explored. Air quality impacts downwind of the fire are addressed using ground-based monitoring site data, satellite smoke products, and the Community Multiscale Air Quality (CMAQ) photochemical grid model

Fast Two-Robot Disk Evacuation with Wireless Communication

In the fast evacuation problem, we study the path planning problem for two robots who want to minimize the worst-case evacuation time on the unit disk. The robots are initially placed at the center of the disk. In order to evacuate, they need to reach an unknown point, the exit, on the boundary of the disk. Once one of the robots finds the exit, it will instantaneously notify the other agent, who will make a beeline to it. The problem has been studied for robots with the same speed~\cite{s1}. We study a more general case where one robot has speed $1$ and the other has speed $s \geq 1$. We provide optimal evacuation strategies in the case that $s \geq c_{2.75} \approx 2.75$ by showing matching upper and lower bounds on the worst-case evacuation time. For $1\leq s < c_{2.75}$, we show (non-matching) upper and lower bounds on the evacuation time with a ratio less than $1.22$. Moreover, we demonstrate that a generalization of the two-robot search strategy from~\cite{s1} is outperformed by our proposed strategies for any $s \geq c_{1.71} \approx 1.71$.Comment: 18 pages, 10 figure

General practice palliative care: Patient and carer expectations, advance care plans and place of death-a systematic review

Background: With an increasing ageing population in most countries, the role of general practitioners (GPs) and general practice nurses (GPNs) in providing optimal end of life (EoL) care is increasingly important. Objective: To explore: (1) patient and carer expectations of the role of GPs and GPNs at EoL; (2) GPs’ and GPNs’ contribution to advance care planning (ACP) and (3) if primary care involvement allows people to die in the place of preference. Method: Systematic literature review. Data sources: Papers from 2000 to 2017 were sought from Medline, Psychinfo, Embase, Joanna Briggs Institute and Cochrane databases. Results: From 6209 journal articles, 51 papers were relevant. Patients and carers expect their GPs to be competent in all aspects of palliative care. They valued easy access to their GP, a multidisciplinary approach to care and well-coordinated and informed care. They also wanted their care team to communicate openly, honestly and empathically, particularly as the patient deteriorated. ACP and the involvement of GPs were important factors which contributed to patients being cared for and dying in their preferred place. There was no reference to GPNs in any paper identified. Conclusions: Patients and carers prefer a holistic approach to care. This review shows that GPs have an important role in ACP and that their involvement facilitates dying in the place of preference. Proactive identification of people approaching EoL is likely to improve all aspects of care, including planning and communicating about EoL. More work outlining the role of GPNs in end of life care is required

Suffix Tree of Alignment: An Efficient Index for Similar Data

We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has $|A|+|B|$ leaves and can be constructed in $O(|A|+|B|)$ time. However, if the two strings are similar, the generalized suffix tree is not efficient because it does not exploit the similarity which is usually represented as an alignment of $A$ and $B$. In this paper we propose a space/time-efficient suffix tree of alignment which wisely exploits the similarity in an alignment. Our suffix tree for an alignment of $A$ and $B$ has $|A| + l_d + l_1$ leaves where $l_d$ is the sum of the lengths of all parts of $B$ different from $A$ and $l_1$ is the sum of the lengths of some common parts of $A$ and $B$. We did not compromise the pattern search to reduce the space. Our suffix tree can be searched for a pattern $P$ in $O(|P|+occ)$ time where $occ$ is the number of occurrences of $P$ in $A$ and $B$. We also present an efficient algorithm to construct the suffix tree of alignment. When the suffix tree is constructed from scratch, the algorithm requires $O(|A| + l_d + l_1 + l_2)$ time where $l_2$ is the sum of the lengths of other common substrings of $A$ and $B$. When the suffix tree of $A$ is already given, it requires $O(l_d + l_1 + l_2)$ time.Comment: 12 page

Superconductivity induced by spark erosion in ZrZn2

We show that the superconductivity observed recently in the weak itinerant ferromagnet ZrZn2 [C. Pfleiderer et al., Nature (London) 412, 58 (2001)] is due to remnants of a superconducting layer induced by spark erosion. Results of resistivity, susceptibility, specific heat and surface analysis measurements on high-quality ZrZn2 crystals show that cutting by spark erosion leaves a superconducting surface layer. The resistive superconducting transition is destroyed by chemically etching a layer of 5 microns from the sample. No signature of superconductivity is observed in rho(T) of etched samples at the lowest current density measured, J=675 Am-2, and at T < 45 mK. EDX analysis shows that spark-eroded surfaces are strongly Zn depleted. The simplest explanation of our results is that the superconductivity results from an alloy with higher Zr content than ZrZn2.Comment: Final published versio