The Densest k-Subhypergraph Problem

The Densest $k$-Subgraph (D$k$S) problem, and its corresponding minimization problem Smallest $p$-Edge Subgraph (S$p$ES), have come to play a central role in approximation algorithms. This is due both to their practical importance, and their usefulness as a tool for solving and establishing approximation bounds for other problems. These two problems are not well understood, and it is widely believed that they do not an admit a subpolynomial approximation ratio (although the best known hardness results do not rule this out). In this paper we generalize both D$k$S and S$p$ES from graphs to hypergraphs. We consider the Densest $k$-Subhypergraph problem (given a hypergraph $(V, E)$, find a subset $W\subseteq V$ of $k$ vertices so as to maximize the number of hyperedges contained in $W$) and define the Minimum $p$-Union problem (given a hypergraph, choose $p$ of the hyperedges so as to minimize the number of vertices in their union). We focus in particular on the case where all hyperedges have size 3, as this is the simplest non-graph setting. For this case we provide an $O(n^{4(4-\sqrt{3})/13 + \epsilon}) \leq O(n^{0.697831+\epsilon})$-approximation (for arbitrary constant $\epsilon > 0$) for Densest $k$-Subhypergraph and an $\tilde O(n^{2/5})$-approximation for Minimum $p$-Union. We also give an $O(\sqrt{m})$-approximation for Minimum $p$-Union in general hypergraphs. Finally, we examine the interesting special case of interval hypergraphs (instances where the vertices are a subset of the natural numbers and the hyperedges are intervals of the line) and prove that both problems admit an exact polynomial time solution on these instances.Comment: 21 page

Essential Tools: Version Control Systems

Did you ever wish you\u27d made a backup copy of a file before changing it? Or before applying a collaborator\u27s modifications? Version control systems make this easier, and do a lot more

A likelihood based comparison of population histories in a parasitoid guild

Little is known about the stability of trophic relationships in complex natural communities over evolutionary timescales. Here, we use sequence data from 18 nuclear loci to reconstruct and compare the intraspecific histories of major Pleistocene refugial populations in the Middle East, the Balkans and Iberia in a guild of four Chalcid parasitoids (Cecidostiba fungosa, Cecidostiba semifascia, Hobbya stenonota and Mesopolobus amaenus) all attacking Cynipid oak galls. We develop a likelihood method to numerically estimate models of divergence between three populations from multilocus data. We investigate the power of this framework on simulated data, and-using triplet alignments of intronic loci-quantify the support for all possible divergence relationships between refugial populations in the four parasitoids. Although an East to West order of population divergence has highest support in all but one species, we cannot rule out alternative population tree topologies. Comparing the estimated times of population splits between species, we find that one species, M. amaenus, has a significantly older history than the rest of the guild and must have arrived in central Europe at least one glacial cycle prior to other guild members. This suggests that although all four species may share a common origin in the East, they expanded westwards into Europe at different times. © 2012 Blackwell Publishing Ltd

Telemedicine Pre and Post Covid-19: Lessons for Commercialisation Based on Previous Use Cases

Telemedicine used to be slow, difficult, expensive and widely neglected by doctors and patients. COVID-19 changed everything; telemedicine is entering a period of rapid economic and business growth. This paper discusses the reasons for change in telemedicine over the last 20 years, through real-life medical technology projects, telemetry, ehealth and health IT. Our methods are based on the analysis of telemedicine projects we have implemented and characteristic historical data.  The results of our investigation demonstrate a clear increase of significance in telemedicine in the present and near future. We envision the evolution of mobile phones to personal telehealth monitors.  Prior to COVID-19, market penetration and economic factors of telemedicine evolved slowly and in an uneven manner on a global scale. Many of the projects remained active only as long as the grant or corporate or national support was provided. The age of novel globally spreading infectious diseases, exemplified by COVID-19, has created an unusual, different setting. Recent pandemics and epidemics have changed global economics significantly and generated a new motivation and a new market with a projected trillion-dollar market value. Post COVID-19, regular and periodic epidemics and pandemics are expected to continue to occur. This will generate an enormous global market for isolated high-tech services, including telemedicine and telemetry

Parameterized Complexity Classification for Interval Constraints

Constraint satisfaction problems form a nicely behaved class of problems that lends itself to complexity classification results. From the point of view of parameterized complexity, a natural task is to classify the parameterized complexity of MinCSP problems parameterized by the number of unsatisfied constraints. In other words, we ask whether we can delete at most $k$ constraints, where $k$ is the parameter, to get a satisfiable instance. In this work, we take a step towards classifying the parameterized complexity for an important infinite-domain CSP: Allen's interval algebra (IA). This CSP has closed intervals with rational endpoints as domain values and employs a set $A$ of 13 basic comparison relations such as ``precedes'' or ``during'' for relating intervals. IA is a highly influential and well-studied formalism within AI and qualitative reasoning that has numerous applications in, for instance, planning, natural language processing and molecular biology. We provide an FPT vs. W[1]-hard dichotomy for MinCSP$(\Gamma)$ for all $\Gamma \subseteq A$. IA is sometimes extended with unions of the relations in $A$ or first-order definable relations over $A$, but extending our results to these cases would require first solving the parameterized complexity of Directed Symmetric Multicut, which is a notorious open problem. Already in this limited setting, we uncover connections to new variants of graph cut and separation problems. This includes hardness proofs for simultaneous cuts or feedback arc set problems in directed graphs, as well as new tractable cases with algorithms based on the recently introduced flow augmentation technique. Given the intractability of MinCSP$(A)$ in general, we then consider (parameterized) approximation algorithms and present a factor-$2$ fpt-approximation algorithm

Rosetta Brains: A Strategy for Molecularly-Annotated Connectomics

We propose a neural connectomics strategy called Fluorescent In-Situ Sequencing of Barcoded Individual Neuronal Connections (FISSEQ-BOINC), leveraging fluorescent in situ nucleic acid sequencing in fixed tissue (FISSEQ). FISSEQ-BOINC exhibits different properties from BOINC, which relies on bulk nucleic acid sequencing. FISSEQ-BOINC could become a scalable approach for mapping whole-mammalian-brain connectomes with rich molecular annotations

Functional Traits of Boreal Species and Adaptation to Local Conditions

Species continuity under the harsh climatic conditions of the boreal forest requires trees to ensure the functioning of two main life processes, namely growth and reproduction. However, species survival becomes a challenge when environmental conditions become unstable and reach the taxa’s ecological tolerance limit. Survival in an unstable environment is possible through the concurring processes of phenotypic plasticity and local adaptation; each process has its advantages and shortcomings. Local adaptation allows attaining the best possible fitness under conditions of limited gene flow and strong directional selection, leading to specific adaptations to the local environment; however, there is a risk of maladaptation when conditions suddenly change. In turn, phenotypic plasticity provides trees an advantage when weather events change rapidly and enables a response expressed by the production of different phenotypes by the same genotype. However, this process is expensive in terms of costs in maintenance and causes developmental instability within the individual. Boreal trees utilize both processes as reflected in variations in their functional traits within the same species. In this chapter, we address the main life processes, presenting the variability of functional traits of flowering and seed production, xylem conductivity, bud and cambium phenology, as well as transpiration and photosynthesis, as a consequence of the interaction of genotype and environment. We describe the practical consequences of a variation in functional traits, as expressed in chemical and mechanical wood properties. Finally, we outline applications and perspectives for managing boreal forests in a context of heterogeneous and changing environmental conditions.Peer reviewe

Recording temporal data with minutes resolution into DNA

Recording complex biological signals is a crucial application of synthetic biology and essential for a deeper understanding of biological processes. An ideal “biorecorder” would have the ability to record biological signals over a wide spatial distribution of cells with high temporal resolution. However, the genetically encoded biorecording tools available have very good spatial resolution (cellular level), but currently rely on turning on and off transcription and translation of a protein (e.g., Cas9 or a recombinase) to record the biological signal, making their temporal resolution on the order of hours. Here we introduce a DNA polymerase based biorecorder that can record cationic concentration fluctuations into DNA sequence with a resolution of ~1 minute. We use a template independent DNA polymerase; terminal deoxynucleotidyl transferase (TdT) that randomly incorporates bases onto a single strand of DNA. The preference of base incorporated by TdT changes with the concentration of cations in TdT’s environment. Therefore, by analyzing a strand of DNA that was extended in fluctuating cation concentrations, we can determine the temporal profile of cation concentration from the bases added. Using this method, we can measure a change in Co2+ concentration during a one hour period with an accuracy of 1 min. We also show the approach works for Zn2+ and Ca2+. We will present our methods for optimizing this biorecorder and characterize its performance in vitro. Recording data onto DNA with minutes time resolution could solve many challenging data acquisition problems in neuroscience and developmental biology, and could aid in the use of DNA as a data storage medium