Range Queries on Uncertain Data

Given a set $P$ of $n$ uncertain points on the real line, each represented by its one-dimensional probability density function, we consider the problem of building data structures on $P$ to answer range queries of the following three types for any query interval $I$: (1) top-$1$ query: find the point in $P$ that lies in $I$ with the highest probability, (2) top-$k$ query: given any integer $k\leq n$ as part of the query, return the $k$ points in $P$ that lie in $I$ with the highest probabilities, and (3) threshold query: given any threshold $\tau$ as part of the query, return all points of $P$ that lie in $I$ with probabilities at least $\tau$. We present data structures for these range queries with linear or nearly linear space and efficient query time.Comment: 26 pages. A preliminary version of this paper appeared in ISAAC 2014. In this full version, we also present solutions to the most general case of the problem (i.e., the histogram bounded case), which were left as open problems in the preliminary versio

The complexity of selection and ranking in X + Y and matrices with sorted columns

AbstractThe complexity of selection is analyzed for two sets, X + Y and matrices with sorted columns. Algorithms are presented that run in time which depends nontrivially on the rank k of the element to be selected and which is sublinear with respect to set cardinality. Identical bounds are also shown for the problem of ranking elements in these sets, and all bounds are shown to be optimal to within a constant multiplicative factor

Successful use of axonal transport for drug delivery by synthetic molecular vehicles

We report the use of axonal transport to achieve intraneural drug delivery. We constructed a novel tripartite complex of an axonal transport facilitator conjugated to a linker molecule bearing up to a hundred reversibly attached drug molecules. The complex efficiently enters nerve terminals after intramuscular or intradermal administration and travels within axonal processes to neuron cell bodies. The tripartite agent provided 100-fold amplification of saturable neural uptake events, delivering multiple drug molecules per complex. _In vivo_, analgesic drug delivery to systemic and to non-targeted neural tissues was greatly reduced compared to existing routes of administration, thus exemplifying the possibility of specific nerve root targeting and effectively increasing the potency of the candidate drug gabapentin 300-fold relative to oral administration

Selection from read-only memory with limited workspace

Given an unordered array of $N$ elements drawn from a totally ordered set and an integer $k$ in the range from $1$ to $N$, in the classic selection problem the task is to find the $k$-th smallest element in the array. We study the complexity of this problem in the space-restricted random-access model: The input array is stored on read-only memory, and the algorithm has access to a limited amount of workspace. We prove that the linear-time prune-and-search algorithm---presented in most textbooks on algorithms---can be modified to use $\Theta(N)$ bits instead of $\Theta(N)$ words of extra space. Prior to our work, the best known algorithm by Frederickson could perform the task with $\Theta(N)$ bits of extra space in $O(N \lg^{*} N)$ time. Our result separates the space-restricted random-access model and the multi-pass streaming model, since we can surpass the $\Omega(N \lg^{*} N)$ lower bound known for the latter model. We also generalize our algorithm for the case when the size of the workspace is $\Theta(S)$ bits, where $\lg^3{N} \leq S \leq N$. The running time of our generalized algorithm is $O(N \lg^{*}(N/S) + N (\lg N) / \lg{} S)$, slightly improving over the $O(N \lg^{*}(N (\lg N)/S) + N (\lg N) / \lg{} S)$ bound of Frederickson's algorithm. To obtain the improvements mentioned above, we developed a new data structure, called the wavelet stack, that we use for repeated pruning. We expect the wavelet stack to be a useful tool in other applications as well.Comment: 16 pages, 1 figure, Preliminary version appeared in COCOON-201

Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas

We investigate analytically and numerically the spatial structure of the non-equilibrium stationary states (NESS) of a point particle moving in a two dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a constant external electric field E as well as a Gaussian thermostat which keeps the speed |v| constant. We show that despite the singular nature of the SRB measure its projections on the space coordinates are absolutely continuous. We further show that these projections satisfy linear response laws for small E. Some of them are computed numerically. We compare these results with those obtained from simple models in which the collisions with the obstacles are replaced by random collisions.Similarities and differences are noted.Comment: 24 pages with 9 figure

Urban vertical air pollution gradient and dynamics investigated with low-cost sensors and large-eddy simulations

A network of five low-cost air pollution sensor (LCS) nodes was deployed vertically on the exterior of the H. C. Ørsted Institute at the University of Copenhagen, Denmark, to investigate the transport of pollution from the road below. All LCS nodes measured PM2.5, NO2, and O3 at 1-min time resolution, and one of them also measured noise. Traffic was monitored with a webcam, where traffic type and levels were derived using a machine-learning algorithm. We investigated how well traffic-related air pollution, noise, and real-time traffic counts serve as proxies for one another. The correlations between NO2, noise, and traffic count exhibited relatively low values when considering all the data. However, these correlations significantly increased under southwesterly wind direction and low wind speed, reaching R2 = 0.40 for NO2 and noise, R2 = 0.51 for NO2 and traffic volume, and R2 = 0.70 for noise and traffic volume. These results indicate a common source, namely traffic, for all three parameters. The five LCS nodes spanning 25 m vertically had extremely low intervariability with minimum R2-values of 0.98 for PM2.5, 0.89 for NO2, and 0.97 for O3. The system could not detect a vertical gradient in pollution levels. Large-eddy simulation model runs using the PALM model system generally supported the lack of gradient observed in measured observations. Under slightly unstable stratification, concentration remained relatively constant with height for southwesterly and southerly winds. Conversely, winds from the north, west, and northwest showed an increase in concentration with height. For other wind directions, the concentration decreased with height by approximately 40 % to 50 %, which is not as strong as for neutral stratification, attributed to enhanced vertical mixing under unstable stratification. Based on the measurements and modeling, we conclude that the vertical concentration profile is very sensitive to stratification, and under these conditions, the concentration outside the window of a fifth-floor office is almost the same as for an office on the ground floor

Reviewing quality of governance:New perspectives and future research

In the concluding chapter, the editors address the central topics of the book as well as some lessons learnt on quality of governance. Public values do matter, but how do they relate (and conflict), with many actors involved in public governance, including at street level and in public-private networks? A broad panorama of values appears to be important for the quality of governance, but the interpretation of the values differs and context is always relevant (macro, meso, and micro). Thus, the work in progress and the chapter define an agenda for future research and offers food for thought for all levels of governance

Laser-initiated decomposition products of indocyanine green (ICG) and carbon black sensitized biological tissues

Organic dyes have found increasing use a s sensitizers in laser surgical procedures, due to their high optical absorbances. Little is known, however, about the nature of the degradation products formed when these dyes are irradiated with a laser. Previous work in our laboratories has shown that irradiation of polymeric and biological tissues with CO2 and Nd:YAG lasers produces a host of volatile and semivolatile by-products, some of which are known to be potential carcinogens. This work focuses on the identification of the chemical by-products formed by diode laser and Nd:YAG laser irradiation of indocyanine green (ICG) and carbon black based ink sensitized tissues, including bone, tendon and sheep\u27s teeth. Samples were mounted in a 0.5-L Pyrex sample chamber equipped with quartz optical windows, charcoal filtered air inlet and an outlet attached to an appropriate sample trap and a constant flow pump. By-products were analyzed by GC/MS and HPLC. Volatiles identified included benzene and formaldehyde. Semi-volatiles included traces of polycyclic aromatics, arising from the biological matrix and inks, as well as fragments of ICG and the carbon ink components. The significance of these results will be discussed, including the necessity of using appropriate evacuation devices when utilizing lasers for surgical procedures