The Tree Inclusion Problem: In Linear Space and Faster

Given two rooted, ordered, and labeled trees $P$ and $T$ the tree inclusion problem is to determine if $P$ can be obtained from $T$ by deleting nodes in $T$. This problem has recently been recognized as an important query primitive in XML databases. Kilpel\"ainen and Mannila [\emph{SIAM J. Comput. 1995}] presented the first polynomial time algorithm using quadratic time and space. Since then several improved results have been obtained for special cases when $P$ and $T$ have a small number of leaves or small depth. However, in the worst case these algorithms still use quadratic time and space. Let $n_S$, $l_S$, and $d_S$ denote the number of nodes, the number of leaves, and the %maximum depth of a tree $S \in \{P, T\}$. In this paper we show that the tree inclusion problem can be solved in space $O(n_T)$ and time: O(\min(l_Pn_T, l_Pl_T\log \log n_T + n_T, \frac{n_Pn_T}{\log n_T} + n_{T}\log n_{T})). This improves or matches the best known time complexities while using only linear space instead of quadratic. This is particularly important in practical applications, such as XML databases, where the space is likely to be a bottleneck.Comment: Minor updates from last tim

String Sanitization Under Edit Distance

Let W be a string of length n over an alphabet Σ, k be a positive integer, and be a set of length-k substrings of W. The ETFS problem asks us to construct a string X_{ED} such that: (i) no string of occurs in X_{ED}; (ii) the order of all other length-k substrings over Σ is the same in W and in X_{ED}; and (iii) X_{ED} has minimal edit distance to W. When W represents an individual’s data and represents a set of confidential substrings, algorithms solving ETFS can be applied for utility-preserving string sanitization [Bernardini et al., ECML PKDD 2019]. Our first result here is an algorithm to solve ETFS in (kn²) time, which improves on the state of the art [Bernardini et al., arXiv 2019] by a factor of |Σ|. Our algorithm is based on a non-trivial modification of the classic dynamic programming algorithm for computing the edit distance between two strings. Notably, we also show that ETFS cannot be solved in (n^{2-δ}) time, for any δ>0, unless the strong exponential time hypothesis is false. To achieve this, we reduce the edit distance problem, which is known to admit the same conditional lower bound [Bringmann and Künnemann, FOCS 2015], to ETFS

NT2 Derived Neuronal and Astrocytic Network Signalling

A major focus of stem cell research is the generation of neurons that may then be implanted to treat neurodegenerative diseases. However, a picture is emerging where astrocytes are partners to neurons in sustaining and modulating brain function. We therefore investigated the functional properties of NT2 derived astrocytes and neurons using electrophysiological and calcium imaging approaches. NT2 neurons (NT2Ns) expressed sodium dependent action potentials, as well as responses to depolarisation and the neurotransmitter glutamate. NT2Ns exhibited spontaneous and coordinated calcium elevations in clusters and in extended processes, indicating local and long distance signalling. Tetrodotoxin sensitive network activity could also be evoked by electrical stimulation. Similarly, NT2 astrocytes (NT2As) exhibited morphology and functional properties consistent with this glial cell type. NT2As responded to neuronal activity and to exogenously applied neurotransmitters with calcium elevations, and in contrast to neurons, also exhibited spontaneous rhythmic calcium oscillations. NT2As also generated propagating calcium waves that were gap junction and purinergic signalling dependent. Our results show that NT2 derived astrocytes exhibit appropriate functionality and that NT2N networks interact with NT2A networks in co-culture. These findings underline the utility of such cultures to investigate human brain cell type signalling under controlled conditions. Furthermore, since stem cell derived neuron function and survival is of great importance therapeutically, our findings suggest that the presence of complementary astrocytes may be valuable in supporting stem cell derived neuronal networks. Indeed, this also supports the intriguing possibility of selective therapeutic replacement of astrocytes in diseases where these cells are either lost or lose functionality

Short-Term Enrichment Makes Male Rats More Attractive, More Defensive and Alters Hypothalamic Neurons

Innate behaviors are shaped by contingencies built during evolutionary history. On the other hand, environmental stimuli play a significant role in shaping behavior. In particular, a short period of environmental enrichment can enhance cognitive behavior, modify effects of stress on learned behaviors and induce brain plasticity. It is unclear if modulation by environment can extend to innate behaviors which are preserved by intense selection pressure. In the present report we investigate this issue by studying effects of relatively short (14-days) environmental enrichment on two prominent innate behaviors in rats, avoidance of predator odors and ability of males to attract mates. We show that enrichment has strong effects on both the innate behaviors: a) enriched males were more avoidant of a predator odor than non-enriched controls, and had a greater rise in corticosterone levels in response to the odor; and b) had higher testosterone levels and were more attractive to females. Additionally, we demonstrate decrease in dendritic length of neurons of ventrolateral nucleus of hypothalamus, important for reproductive mate-choice and increase in the same in dorsomedial nucleus, important for defensive behavior. Thus, behavioral and hormonal observations provide evidence that a short period of environmental manipulation can alter innate behaviors, providing a good example of gene-environment interaction

Decompressing lempel-ziv compressed text

We consider the problem of decompressing the Lempel-Ziv 77 representation of a string S of length n using a working space as close as possible to the size z of the input. The folklore solution for the problem runs in O(n) time but requires random access to the whole decompressed text. Another folklore solution is to convert LZ77 into a grammar of size O(z log(n/z)) and then stream S in linear time. In this paper, we show that O(n) time and O(z) working space can be achieved for constant-size alphabets. On general alphabets of size \u3c3, we describe (i) a trade-off achieving O(n log^\u3b4 \u3c3) time and O(z log^1-\u3b4 \u3c3) space for any 0 64 \u3b4 64 1, and (ii) a solution achieving O(n) time and O(z log log (n/z)) space. The latter solution, in particular, dominates both folklore algorithms for the problem. Our solutions can, more generally, extract any specified subsequence of S with little overheads on top of the linear running time and working space. As an immediate corollary, we show that our techniques yield improved results for pattern matching problems on LZ77-compressed text

Mikroimplantate in der Medizintechnik mit drahtloser Daten- und Energieübertragung

Intelligent implants are implantable micro sensors or micro actuators with integrated signal conditioning and wireless data transmission. They constitute an indispensable part of modern medical diagnostics and therapy. While cardiac pacemakers or defibrillators offer sufficient space for the integration of a battery, micro implants like cochlear implant, retinal implant or such for the monitoring of physiological parameters have to be designed as passive transponder. Power and data are transmitted using inductive coupling. In order to ensure an interference-proof communication all data are digitized, encoded, and secured by a check sum before transmission. The potential of the micro implant technology is outlined by the example of a micro sensor system for monitoring of patients with high blood pressure and the example of a micro stimulation system as a visual prosthesis for patients suffering from retinitis pigmentosa

Decompressing lempel-ziv compressed text

We consider the problem of decompressing the Lempel-Ziv 77 representation of a string S of length n using a working space as close as possible to the size z of the input. The folklore solution for the problem runs in O(n) time but requires random access to the whole decompressed text. Another folklore solution is to convert LZ77 into a grammar of size O(z log(n/z)) and then stream S in linear time. In this paper, we show that O(n) time and O(z) working space can be achieved for constant-size alphabets. On general alphabets of size σ, we describe (i) a trade-off achieving O(n log^δ σ) time and O(z log^1-δ σ) space for any 0≤ δ≤ 1, and (ii) a solution achieving O(n) time and O(z log log (n/z)) space. The latter solution, in particular, dominates both folklore algorithms for the problem. Our solutions can, more generally, extract any specified subsequence of S with little overheads on top of the linear running time and working space. As an immediate corollary, we show that our techniques yield improved results for pattern matching problems on LZ77-compressed text

Optical measurements of orientational order in uniaxial and biaxial nematic liquid crystals

The use of optical methods to study the orientational order in nematic liquid crystals is both convenient and powerful. Some of the earliest approaches made use of measurements of the refractive index anisotropy, following the methodology of Halle [1] to measure the order parameter, [image omitted]. This method is reviewed briefly and some typical areas of application are presented. Raman spectroscopy is a second approach discussed in this paper. Although technically a more complex methodology, Raman spectroscopy has the significant advantage that in addition to being able to measure [image omitted] it is also possible to determine [image omitted]. A review of current approaches is presented. Very recently, it has been shown that polarised Raman spectroscopy can be employed to determine biaxial order parameters in liquid crystals. The methodology is described, and data are presented for such measurements on a series of bent-core nematic materials that could exhibit the elusive biaxial nematic phase

Unary Words Have the Smallest Levenshtein k-Neighbourhoods

The edit distance (a.k.a. the Levenshtein distance) between two words is defined as the minimum number of insertions, deletions or substitutions of letters needed to transform one word into another. The Levenshtein k-neighbourhood of a word w is the set of words that are at edit distance at most k from w. This is perhaps the most important concept underlying BLAST, a widely-used tool for comparing biological sequences. A natural combinatorial question is to ask for upper and lower bounds on the size of this set. The answer to this question has important algorithmic implications as well. Myers notes that "such bounds would give a tighter characterisation of the running time of the algorithm" behind BLAST. We show that the size of the Levenshtein k-neighbourhood of any word of length n over an arbitrary alphabet is not smaller than the size of the Levenshtein k-neighbourhood of a unary word of length n, thus providing a tight lower bound on the size of the Levenshtein k-neighbourhood. We remark that this result was posed as a conjecture by Dufresne at WCTA 2019. 2012 ACM Subject Classification Theory of computation ! Pattern matching

Thermotropic biaxial nematic order parameters and phase transitions deduced by Raman scattering

Raman Scattering was used to investigate biaxiality in the nematic phase formed by the bent-core material, C5-Ph-ODBP-Ph-OC12. Linearly polarised light was normally incident on a homogeneously aligned sample, and the depolarisation ratio was measured over a 360 degrees rotation of the incident polarisation for the Raman-active phenyl stretching mode. By modeling the bent-core structure and fitting to the depolarisation data, both the uniaxial ([P(200)] and [P(400)]) and biaxial ([P(220)], [P(420)] and [P(440)]) order parameters, are deduced. We show unequivocally the presence of a uniaxial to biaxial nematic phase transition approximately 30 degrees C above the underlying smectic phase. Further, we report the temperature evolution of the biaxial and uniaxial order parameters, which increase in magnitude continuously with reducing temperature, reaching values of 0.1, -0.15 and -0.18 for [P(220)], [P(420)] and [P(440)], respectively. Copyright (c) EPLA, 2008