Inapproximability of the Standard Pebble Game and Hard to Pebble Graphs

Pebble games are single-player games on DAGs involving placing and moving pebbles on nodes of the graph according to a certain set of rules. The goal is to pebble a set of target nodes using a minimum number of pebbles. In this paper, we present a possibly simpler proof of the result in [CLNV15] and strengthen the result to show that it is PSPACE-hard to determine the minimum number of pebbles to an additive $n^{1/3-\epsilon}$ term for all $\epsilon > 0$, which improves upon the currently known additive constant hardness of approximation [CLNV15] in the standard pebble game. We also introduce a family of explicit, constant indegree graphs with $n$ nodes where there exists a graph in the family such that using constant $k$ pebbles requires $\Omega(n^k)$ moves to pebble in both the standard and black-white pebble games. This independently answers an open question summarized in [Nor15] of whether a family of DAGs exists that meets the upper bound of $O(n^k)$ moves using constant $k$ pebbles with a different construction than that presented in [AdRNV17].Comment: Preliminary version in WADS 201

Quantitative Models and Implicit Complexity

We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by one of us), Light Affine Logic and Soft Affine Logic. The proofs are based on a common semantical framework which is merely instantiated in four different ways. The framework consists of an innovative modification of realizability which allows us to use resource-bounded computations as realisers as opposed to including all Turing computable functions as is usually the case in realizability constructions. For example, all realisers in the model for LFPL are polynomially bounded computations whence soundness holds by construction of the model. The work then lies in being able to interpret all the required constructs in the model. While being the first entirely semantical proof of polytime soundness for light logi cs, our proof also provides a notable simplification of the original already semantical proof of polytime soundness for LFPL. A new result made possible by the semantic framework is the addition of polymorphism and a modality to LFPL thus allowing for an internal definition of inductive datatypes.Comment: 29 page

Searching of gapped repeats and subrepetitions in a word

A gapped repeat is a factor of the form $uvu$ where $u$ and $v$ are nonempty words. The period of the gapped repeat is defined as $|u|+|v|$. The gapped repeat is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its period. The gapped repeat is called $\alpha$-gapped if its period is not greater than $\alpha |v|$. A $\delta$-subrepetition is a factor which exponent is less than 2 but is not less than $1+\delta$ (the exponent of the factor is the quotient of the length and the minimal period of the factor). The $\delta$-subrepetition is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its minimal period. We reveal a close relation between maximal gapped repeats and maximal subrepetitions. Moreover, we show that in a word of length $n$ the number of maximal $\alpha$-gapped repeats is bounded by $O(\alpha^2n)$ and the number of maximal $\delta$-subrepetitions is bounded by $O(n/\delta^2)$. Using the obtained upper bounds, we propose algorithms for finding all maximal $\alpha$-gapped repeats and all maximal $\delta$-subrepetitions in a word of length $n$. The algorithm for finding all maximal $\alpha$-gapped repeats has $O(\alpha^2n)$ time complexity for the case of constant alphabet size and $O(n\log n + \alpha^2n)$ time complexity for the general case. For finding all maximal $\delta$-subrepetitions we propose two algorithms. The first algorithm has $O(\frac{n\log\log n}{\delta^2})$ time complexity for the case of constant alphabet size and $O(n\log n +\frac{n\log\log n}{\delta^2})$ time complexity for the general case. The second algorithm has $O(n\log n+\frac{n}{\delta^2}\log \frac{1}{\delta})$ expected time complexity

A model sensitivity study of the impact of clouds on satellite detection and retrieval of volcanic ash

Volcanic ash is commonly observed by infrared detectors on board Earth-orbiting satellites. In the presence of ice and/or liquid-water clouds, the detected volcanic ash signature may be altered. In this paper the sensitivity of detection and retrieval of volcanic ash to the presence of ice and liquid-water clouds was quantified by simulating synthetic equivalents to satellite infrared images with a 3-D radiative transfer model. The sensitivity study was made for the two recent eruptions of Eyjafjallajokull (2010) and Grimsvotn (2011) using realistic water and ice clouds and volcanic ash clouds. The water and ice clouds were taken from European Centre for Medium-RangeWeather Forecast (ECMWF) analysis data and the volcanic ash cloud fields from simulations by the Lagrangian particle dispersion model FLEXPART. The radiative transfer simulations were made both with and without ice and liquid-water clouds for the geometry and channels of the Spinning Enhanced Visible and Infrared Imager (SEVIRI). The synthetic SEVIRI images were used as input to standard reverse absorption ash detection and retrieval methods. Ice and liquid-water clouds were on average found to reduce the number of detected ash-affected pixels by 6-12 %. However, the effect was highly variable and for individual scenes up to 40% of pixels with mass loading > 0 : 2 gm 2 could not be detected due to the presence of water and ice clouds. For coincident pixels, i. e. pixels where ash was both present in the FLEXPART (hereafter referred to as "Flexpart") simulation and detected by the algorithm, the presence of clouds overall increased the retrieved mean mass loading for the Eyjafjallajokull (2010) eruption by about 13 %,while for the Grimsvotn (2011) eruption ash-mass loadings the effect was a 4% decrease of the retrieved ash-mass loading. However, larger differences were seen between scenes (standard deviations of +/- 30 and +/- 20% for Eyjafjallajokull and Grimsvotn, respectively) and even larger ones within scenes. The impact of ice and liquid-water clouds on the detection and retrieval of volcanic ash, implies that to fully appreciate the location and amount of ash, hyperspectral and spectral band measurements by satellite instruments should be combined with ash dispersion modelling

Transcriptionally active enhancers in human cancer cells

The growth of human cancer cells is driven by aberrant enhancer and gene transcription activity. Here, we use transient transcriptome sequencing (TT-seq) to map thousands of transcriptionally active putative enhancers in fourteen human cancer cell lines covering seven types of cancer. These enhancers were associated with cell type-specific gene expression, enriched for genetic variants that predispose to cancer, and included functionally verified enhancers. Enhancer-promoter (E-P) pairing by correlation of transcription activity revealed similar to 40,000 putative E-P pairs, which were depleted for housekeeping genes and enriched for transcription factors, cancer-associated genes, and 3D conformational proximity. The cell type specificity and transcription activity of target genes increased with the number of paired putative enhancers. Our results represent a rich resource for future studies of gene regulation by enhancers and their role in driving cancerous cell growth.Peer reviewe

MINSTED nanoscopy enters the Ångström localization range

We report all-optical, room-temperature localization of fluorophores with precision in the Ångström range. These precisions are attained in a STED microscope, by encircling the fluorophore with the low-intensity edge of the STED donut beam, while constantly increasing the absolute donut power. Individual fluorophores bound to a DNA strand are localized with σ = 4.7 Å, corresponding to a fraction of the fluorophore size, with only 2,000 detected photons. MINSTED fluorescence nanoscopy with single-digit nanometer resolution is exemplified by imaging nuclear pore complexes and the distribution of nuclear lamin in mammalian cells labeled by transient DNA hybridization. Since our experiments yield a localization precision σ = 2.3 Å, estimated for 10,000 detected photons, we anticipate that MINSTED will open up entirely new areas of application in the study of macromolecular complexes in cells

A taste of the deep-sea: The roles of gustatory and tactile searching behaviour in the grenadier fish <i>Coryphaenoides armatus</i>

The deep-sea grenadier fishes (Coryphaenoides spp.) are among the dominant predators and scavengers in the ocean basins that cover much of Earth's surface. Baited camera experiments were used to study the behaviour of these fishes. Despite the apparent advantages of rapidly consuming food, grenadiers attracted to bait spend a large proportion of their time in prolonged periods of non-feeding activity. Video analysis revealed that fish often adopted a head-down swimming attitude (mean of 21.3 degrees between the fish and seafloor), with swimming velocity negatively related to attitude. The fish also swam around and along vertical and horizontal structures of the lander with their head immediately adjacent to the structure. We initially hypothesised that this behaviour was associated with the use of the short chin barbel in foraging. Barbel histology showed numerous taste buds in the skin, and a barbel nerve with about 20,000 axons in adult fish. A tracing experiment in one undamaged animal revealed the termination fields of the barbel neurons in the trigeminal and rhombencephalic regions, indicating both a mechanoreceptory and a gustatory role for the barbel. Our conclusion was that olfactory foraging becomes ineffective at close ranges and is followed by a search phase using tactile and gustatory sensing by the barbel. The development of this sensory method probably co-evolved alongside behavioural changes in swimming mechanics to allow postural stability at low swimming speeds

Active Electric Imaging: Body-Object Interplay and Object's “Electric Texture”

This article deals with the role of fish's body and object's geometry on determining the image spatial shape in pulse Gymnotiforms. This problem was explored by measuring local electric fields along a line on the skin in the presence and absence of objects. We depicted object's electric images at different regions of the electrosensory mosaic, paying particular attention to the perioral region where a fovea has been described. When sensory surface curvature increases relative to the object's curvature, the image details depending on object's shape are blurred and finally disappear. The remaining effect of the object on the stimulus profile depends on the strength of its global polarization. This depends on the length of the object's axis aligned with the field, in turn depending on fish body geometry. Thus, fish's body and self-generated electric field geometries are embodied in this “global effect” of the object. The presence of edges or local changes in impedance at the nearest surface of closely located objects adds peaks to the image profiles (“local effect” or “object's electric texture”). It is concluded that two cues for object recognition may be used by active electroreceptive animals: global effects (informing on object's dimension along the field lines, conductance, and position) and local effects (informing on object's surface). Since the field has fish's centered coordinates, and electrosensory fovea is used for exploration of surfaces, fish fine movements are essential to perform electric perception. We conclude that fish may explore adjacent objects combining active movements and electrogenesis to represent them using electrosensory information

Difference or delay? A comparison of Bayley-III Cognition item scores of young children with and without developmental disabilities

The “difference or delay paradigm” focuses on the question of whether children with develop-mental disabilities (DD) develop in a way that is only delayed, compared to typically developingchildren, or also qualitatively different. The current study aimed to examine whether qualitativedifferences exist in cognitive development of young children with and without DD on the basis ofitem scores on the Dutch Bayley-III Cognition scale. Differential item functioning was identifiedfor 15 of the 91 items. The presence of DD was related to a higher number of Guttman errors,hinting at more deviation in the order of skill development. An interaction between group (i.e.,with or without DD) and developmental quotient appeared to predict the number of Guttmanerrors. DD was related to a higher number of Guttman errors for the whole range of develop-mental quotients; children with DD with a small developmental quotient had the highest number.Combined, the results mean that qualitative differences in development are not to be excluded,especially in cases of severe developmental disabilities. When using the Bayley-III in dailypractice, the possibility needs to be taken into account that the instruments’ assumption of a fixedorder in skill development does not hold