Deterministic and Probabilistic Binary Search in Graphs

We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to querying a node $q$, the algorithm learns either that $q$ is the target, or is given an edge out of $q$ that lies on a shortest path from $q$ to the target. We study this problem in a general noisy model in which each query independently receives a correct answer with probability $p > \frac{1}{2}$ (a known constant), and an (adversarial) incorrect one with probability $1-p$. Our main positive result is that when $p = 1$ (i.e., all answers are correct), $\log_2 n$ queries are always sufficient. For general $p$, we give an (almost information-theoretically optimal) algorithm that uses, in expectation, no more than $(1 - \delta)\frac{\log_2 n}{1 - H(p)} + o(\log n) + O(\log^2 (1/\delta))$ queries, and identifies the target correctly with probability at leas $1-\delta$. Here, $H(p) = -(p \log p + (1-p) \log(1-p))$ denotes the entropy. The first bound is achieved by the algorithm that iteratively queries a 1-median of the nodes not ruled out yet; the second bound by careful repeated invocations of a multiplicative weights algorithm. Even for $p = 1$, we show several hardness results for the problem of determining whether a target can be found using $K$ queries. Our upper bound of $\log_2 n$ implies a quasipolynomial-time algorithm for undirected connected graphs; we show that this is best-possible under the Strong Exponential Time Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs with non-uniform node querying costs, the problem is PSPACE-complete. For a semi-adaptive version, in which one may query $r$ nodes each in $k$ rounds, we show membership in $\Sigma_{2k-1}$ in the polynomial hierarchy, and hardness for $\Sigma_{2k-5}$

XEN glaucoma treatment system in the management of refractory glaucomas: a short review on trial data and potential role in clinical practice

The recent development of new devices that are significantly less invasive, collectively termed minimally invasive glaucoma surgery, offers new perspective of intraocular pressure reduction with less risk, short operating times, and rapid recovery. The aim of this work is to provide a panoramic review of the currently published clinical data to assess the potential role of XEN gel stent (Allergan PLC, Irvine, CA, USA) in the management of glaucoma, which is the only filtering minimally invasive glaucoma surgery device that allows the subconjunctival filtration. The ab interno placement of the XEN gel stent offers an alternative for lowering intraocular pressure in refractory glaucoma as a final step, and in patients intolerant to medical therapy as an early surgical approach with minimum conjunctival tissue disruption, restricted flow to avoid hypotony, and long-term safety

Airborne pollen in Alpine sites

Airborne pollen is usually monitored at urban centers, where most people live, to provide information on types and amount of allergenic pollen. Thus, very few aerobiological data are available for remote, mountainous sites. This study aims to characterize the biological quality of the air in an alpine valley in Trentino (North Italy), a region highly interested by the presence of tourists (e.g., 9.3 million overnight stays registered during June - September 2021). Materials and Methods An aerobiological study was carried out during late spring and summer in 2020 and 2021 in Val di Rabbi, an alpine valley located in the Trentino sector of Stelvio National Park. Gravitational Sigma2 samplers were selected for the survey, for their reliability and efficiency (VDI_2119 2013) and easy handling at remote sites (Gottardini et al. 2021), and installed at 2 m above ground level in 5 sites located at altitudes ranging from 700 to 2000 m a.s.l. Sampling surfaces, treated with an adhesive medium, were analyzed by optical microscopy (OM; 400×; Leitz Diaplan) for pollen identification and count (weekly samples); the average daily sedimentation rate (P cm–2 d–1 ) was calculated for the June-August period. In 2021, an active Hirst-type sampler was concurrently installed in one of the five sites (daily samples). Samples were processed and analyzed following conventional techniques and standardized protocols (UNI EN 16868:2019). Results and Discussion In the two study periods, the number of identified pollen taxa ranged from 25 at the highest elevation site (2000 m a.s.l.) to 39 at the lowest elevation (700 m a.s.l.). The proportion of arboreal pollen slightly decreased with the altitude, from 51% to 42%. The three most abundant pollen taxa were pine (Pinus), grasses (Poaceae) and neetle (Urticaceae), even if in different proportion at each site. The only grass and nettle allergenic pollen represented on average the 52% of the total pollen. The pollen season peak for grasses showed a delay of about 4 days every 100 m of elevation (Figure 1). 47 pollen taxa were identified, by active sampling, 10 more than by the passive one. The most abundant pollen taxa detected by active sampling were pine, grasses, and nettle, as for passive sampling, with the last two representing even the 71% of the total. The pollen season peak for grasses was on 22nd June, coherently with the passive sampling results at the same site. Conclusions Our mountain aerobiological study reveals the presence of allergenic pollen even at high altitude, with noteworthy shifts in the pollen season. The surveyed data can be further exploited for studying the plant biodiversity in remote areas, as well as to provide useful information for allergic tourist and hikers. Moreover, passive sampling proved to be a feasible solution for aerobiological studies in remote or orographically complex areas, typically excluded in routine air quality monitoring. References Gottardini et al. (2021). AAQR, Vol. 21, https://doi.org/10.4209/aaqr.210010 VDI_2119 (2013). Ambient air measurements. Sampling of atmospheric particles > 2.5 μm on an acceptor surface using the Sigma-2 passive sampler. Characterization by optical microscopy and calculation of number settling rate and mass concentration. ICS: 13.040.01. Beuth Verlag, Berlin. Germany. Acknowledgements The study was partially financed by Provincia Autonoma di Trento (IT). We are grateful to Mattia Precazzini and Gabriele Canella for the support in field work, and to Maria Cristina Viola for the microscope pollen analysis

A conceptual constitutive model unifying slurried (saturated), compacted (unsaturated) and dry states

Reconstituted and compacted soils are commonly assumed to exhibit a fundamentally different behaviour due to different microstructure. However, inspection of pore size distribution of the same soil in compacted and reconstituted states suggests that the boundary between these two states is more blurred. This paper explores the continuity between the microstructure of reconstituted and compacted states of kaolin clay and formulates a conceptual constitutive model unifying these states. Clay samples were prepared by saturating the pore space with different fluids (water, acetone and air) and the effect of pore-fluid fraction on the micro- and macroscale response of the clay was investigated experimentally. A conceptual constitutive model for unsaturated clays for quasi-isotropic stress states was therefore formulated, which allows the modelling of various unsaturated hydro-mechanical paths based on constitutive parameters only derived from the compression behaviour of clay under dry and saturated conditions (testing on samples formed from dry powder and slurry, respectively)

Hide-and-seek in a highly human-dominated landscape: insights into movement patterns and selection of resting sites of rehabilitated wolves (Canis lupus) in Northern Italy

Assessing the behavioural responses of floating wolves to human presence is crucial for investigating the chance of wolf populations expanding into urbanised landscapes. We studied the movement ecology of three rehabilitated wolves in a highly human-dominated landscape (Po Plain, Italy) to explore wolf’s plasticity amid widespread human pressure. To reach this aim, we estimated individual 95% utilisation distributions (UD) after the release and inspected both 95% UDs and net squared displacements to identify individual movement patterns; tested for differences in movement patterns during day and night; and analysed the selection of resting sites during dispersal movement in a highly human-altered environment. Both the 95% UDs and step lengths were smaller for wolves settling in suitable areas than for those settling in more urbanised areas. All wolves exhibited strong temporal segregation with humans during all movement phases, particularly while dispersing across highly urbanised areas. Main roads and proximity to built-up areas were shown to limit wolves’ dispersal, whereas small-wooded patches that provide shelter during rest facilitated long-distance movements. This study provides important insights into wolf movement and settling in urban and peri-urban areas, providing critical knowledge to promote human–carnivore coexistenc

A photonic bandgap resonator to facilitate GHz frequency conductivity experiments in pulsed magnetic fields

We describe instrumentation designed to perform millimeter-wave conductivity measurements in pulsed high magnetic fields at low temperatures. The main component of this system is an entirely non-metallic microwave resonator. The resonator utilizes periodic dielectric arrays (photonic bandgap structures) to confine the radiation, such that the resonant modes have a high Q-factor, and the system possesses sufficient sensitivity to measure small samples within the duration of a magnet pulse. As well as measuring the sample conductivity to probe orbital physics in metallic systems, this technique can detect the sample permittivity and permeability allowing measurement of spin physics in insulating systems. We demonstrate the system performance in pulsed magnetic fields with both electron paramagnetic resonance experiments and conductivity measurements of correlated electron systems.Comment: Submitted to the Review of Scientific instrument

Apartment performance and employment distribution : a study of two cities

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Architecture, 1988.Includes bibliographical references.by Daniel A. Pedrotti, Jr.M.S