Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations

Cake cutting is one of the most fundamental settings in fair division and mechanism design without money. In this paper, we consider different levels of three fundamental goals in cake cutting: fairness, Pareto optimality, and strategyproofness. In particular, we present robust versions of envy-freeness and proportionality that are not only stronger than their standard counter-parts but also have less information requirements. We then focus on cake cutting with piecewise constant valuations and present three desirable algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time, robust envy-free, and non-wasteful. It relies on parametric network flows and recent generalizations of the probabilistic serial algorithm. For the subdomain of piecewise uniform valuations, we show that it is also group-strategyproof. Then, we show that there exists an algorithm (MEA) that is polynomial-time, envy-free, proportional, and Pareto optimal. MEA is based on computing a market-based equilibrium via a convex program and relies on the results of Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise uniform valuations. We then present an algorithm CSD and a way to implement it via randomization that satisfies strategyproofness in expectation, robust proportionality, and unanimity for piecewise constant valuations. For the case of two agents, it is robust envy-free, robust proportional, strategyproof, and polynomial-time. Many of our results extend to more general settings in cake cutting that allow for variable claims and initial endowments. We also show a few impossibility results to complement our algorithms.Comment: 39 page

Social Welfare in One-Sided Matching Mechanisms

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of $\Omega(\sqrt{n})$ on the Price of Anarchy, which applies to all mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and Random Priority, achieve a matching upper bound. We extend our lower bound to the Price of Stability of a large class of mechanisms that satisfy a common proportionality property, and show stronger bounds on the Price of Anarchy of all deterministic mechanisms

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of the pyrochlore specific heat correcte

Trafficking activity of myosin XXI is required in assembly of Leishmania flagellum

Actin-based myosin motors have a pivotal role in intracellular trafficking in eukaryotic cells. The parasitic protozoan organism Leishmania expresses a novel class of myosin, myosin XXI (Myo21), which is preferentially localized at the proximal region of the flagellum. However, its function in this organism remains largely unknown. Here, we show that Myo21 interacts with actin, and its expression is dependent of the growth stage. We further reveal that depletion of Myo21 levels results in impairment of the flagellar assembly and intracellular trafficking. These defects are, however, reversed by episomal complementation. Additionally, it is shown that deletion of the Myo21 gene leads to generation of ploidy, suggesting an essential role of Myo21 in survival of Leishmania cells. Together, these results indicate that actin-dependent trafficking activity of Myo21 is essentially required during assembly of the Leishmania flagellum

NGS-QCbox and Raspberry for Parallel, Automated and Rapid Quality Control Analysis of Large-Scale Next Generation Sequencing (Illumina) Data

Rapid popularity and adaptation of next generation sequencing (NGS) approaches have generated huge volumes of data. High throughput platforms like Illumina HiSeq produce terabytes of raw data that requires quick processing. Quality control of the data is an important component prior to the downstream analyses. To address these issues, we have developed a quality control pipeline, NGS-QCbox that scales up to process hundreds or thousands of samples. Raspberry is an in-house tool, developed in C language utilizing HTSlib (v1.2.1) (http://htslib.org), for computing read/base level statistics. It can be used as stand-alone application and can process both compressed and uncompressed FASTQ format files. NGS-QCbox integrates Raspberry with other open-source tools for alignment (Bowtie2), SNP calling (SAMtools) and other utilities (bedtools) towards analyzing raw NGS data at higher efficiency and in high-throughput manner. The pipeline implements batch processing of jobs using Bpipe (https://github.com/ssadedin/bpipe) in parallel and internally, a fine grained task parallelization utilizing OpenMP. It reports read and base statistics along with genome coverage and variants in a user friendly format. The pipeline developed presents a simple menu driven interface and can be used in either quick or complete mode. In addition, the pipeline in quick mode outperforms in speed against other similar existing QC pipeline/tools. The NGS-QCbox pipeline, Raspberry tool and associated scripts are made available at the URL https://github.com/CEG-ICRISAT/NGS-QCbox and https://github.com/ CEG-ICRISAT/Raspberry for rapid quality control analysis of large-scale next generation sequencing (Illumina) data

Diabetes Alters Contraction-Induced Mitogen Activated Protein Kinase Activation in the Rat Soleus and Plantaris

The prescription of anaerobic exercise has recently been advocated for the management of diabetes; however exercise-induced signaling in diabetic muscle remains largely unexplored. Evidence from exercise studies in nondiabetics suggests that the extracellular-signal-regulated kinases (Erk1/2), p38, and c-JUN NH2-terminal kinase (Jnk) mitogen-activated protein kinases (MAPKs) are important regulators of muscle adaptation. Here, we compare the basal and the in situ contraction-induced phosphorylation of Erk1/2- p38- and Jnk-MAPK and their downstream targets (p90rsk and MAPKAP-K2) in the plantaris and soleus muscles of normal and obese (fa/fa) Zucker rats. Compared to lean animals, the time course and magnitude of Erk1/2, p90rsk and p38 phosphorylation to a single bout of contractile stimuli were greater in the plantaris of obese animals. Jnk phosphorylation in response to contractile stimuli was muscle-type dependent with greater increases in the plantaris than the soleus. These results suggest that diabetes alters intramuscular signaling processes in response to a contractile stimulus

Association of Gene with Cytoplasmic Male Sterility in Pigeonpea

Cytoplasmic male sterility (CMS) has been exploited in the commercial pigeonpea [Cajanus cajan (L.) Millsp.] hybrid breeding system; however, the molecular mechanism behind this system is unknown. To understand the underlying molecular mechanism involved in A4 CMS system derived from C. cajanifolius (Haines) Maesen, 34 mitochondrial genes were analyzed for expression profiling and structural variation analysis between CMS line (ICRISAT Pigeonpea A line, ICPA 2039) and its cognate maintainer (ICPB 2039). Expression profiling of 34 mitochondrial genes revealed nine genes with significant fold differential gene expression at P ≤ 0.01, including one gene, nad4L, with 1366-fold higher expression in CMS line as compared with the maintainer. Structural variation analysis of these mitochondrial genes identified length variation between ICPA 2039 and ICPB 2039 for nad7a (subunit of nad7 gene). Sanger sequencing of nad4L and nad7a genes in the CMS and the maintainer lines identified two single nucleotide polymorphisms (SNPs) in upstream region of nad4L and a deletion of 10 bp in nad7a in the CMS line. Protein structure evaluation showed conformational changes in predicted protein structures for nad7a between ICPA 2039 and ICPB 2039 lines. All above analyses indicate association of nad7a gene with the CMS for A4 cytoplasm in pigeonpea. Additionally, one polymerase chain reaction (PCR) based Indel marker (nad7a_del) has been developed and validated for testing genetic purity of A4 derived CMS lines to strengthen the commercial hybrid breeding program in pigeonpea

Effect of varying skin surface electrode position on electroretinogram responses recorded using a handheld stimulating and recording system

Purpose A handheld device (the RETeval system, LKC Technologies) aims to increase the ease of electroretinogram (ERG) recording by using specially designed skin electrodes, rather than corneal electrodes. We explored effects of electrode position on response parameters recorded using this device. Methods Healthy adult twins were recruited from the TwinsUK cohort and underwent recording of light-adapted flicker ERGs (corresponding to international standard stimuli). In Group 1, skin electrodes were placed in a “comfortable” position, which was up to 20 mm below the lid margin. For subsequent participants (Group 2), the electrode was positioned 2 mm from the lid margin as recommended by the manufacturer. Amplitudes and peak times (averaged from both eyes) were compared between groups after age-matching and inclusion of only one twin per pair. Light-adapted flicker and flash ERGs were recorded for an additional 10 healthy subjects in two consecutive recording sessions: in the test eye, electrode position was varied from 2 to 10–20 mm below the lid margin between sessions; in the fellow (control) eye, the electrode was 2 mm below the lid margin throughout. Amplitudes and peak times (test eye normalised to control eye) were compared for the two sessions. Results Including one twin per pair, and age-matching yielded 28 individuals per group. Flicker ERG amplitudes were significantly lower for Group 1 than Group 2 participants (p = 0.0024). However, mean peak times did not differ between groups (p = 0.54). For the subjects in whom electrode position was changed between recording sessions, flash and flicker amplitudes were significantly lower when positioned further from the lid margin (p  0.5). Conclusions Moving the skin electrodes further from the lid margin significantly reduces response amplitudes, highlighting the importance of consistent electrode positioning. However, this does not significantly affect peak times. Thus, it may be feasible to adopt a more comfortable position in participants who cannot tolerate the recommended position if analysis is restricted to peak time parameters

CicArVarDB: SNP and InDel database for advancing genetics research and breeding applications in chickpea

Molecular markers are valuable tools for breeders to help accelerate crop improvement. High throughput sequencing technologies facilitate the discovery of large-scale variations such as single nucleotide polymorphisms (SNPs) and simple sequence repeats (SSRs). Sequencing of chickpea genome along with re-sequencing of several chickpea lines has enabled the discovery of 4.4 million variations including SNPs and InDels. Here we report a repository of 1.9 million variations (SNPs and InDels) anchored on eight pseudomolecules in a custom database, referred as CicArVarDB that can be accessed at http://cicarvardb.icrisat.org/. It includes an easy interface for users to select variations around specific regions associated with quantitative trait loci, with embedded webBLAST search and JBrowse visualisation. We hope that this database will be immensely useful for the chickpea research community for both advancing genetics research as well as breeding applications for crop improvement

Draft genome sequence of Sclerospora graminicola, the pearl millet downy mildew pathogen:Genome sequence of pearl millet downy mildew pathogen

Sclerospora graminicola pathogen is one of the most important biotic production constraints of pearl millet worldwide. We report a de novo whole genome assembly and analysis of pathotype 1. The draft genome assembly contained 299,901,251 bp with 65,404 genes. Pearl millet [Pennisetum glaucum (L.) R. Br.], is an important crop of the semi-arid and arid regions of the world. It is capable of growing in harsh and marginal environments with highest degree of tolerance to drought and heat among cereals (1). Downy mildew is the most devastating disease of pearl millet caused by Sclerospora graminicola (sacc. Schroet), particularly on genetically uniform hybrids. Estimated annual grain yield loss due to downy mildew is approximately 10?80 % (2-7). Pathotype 1 has been reported to be the highly virulent pathotype of Sclerospora graminicola in India (8). We report a de novo whole genome assembly and analysis of Sclerospora graminicola pathotype 1 from India. A susceptible pearl millet genotype Tift 23D2B1P1-P5 was used for obtaining single-zoospore isolates from the original oosporic sample. The library for whole genome sequencing was prepared according to the instructions by NEB ultra DNA library kit for Illumina (New England Biolabs, USA). The libraries were normalised, pooled and sequenced on Illumina HiSeq 2500 (Illumina Inc., San Diego, CA, USA) platform at 2 x100 bp length. Mate pair (MP) libraries were prepared using the Nextera mate pair library preparation kit (Illumina Inc., USA). 1 ?g of Genomic DNA was subject to tagmentation and was followed by strand displacement. Size selection tagmented/strand displaced DNA was carried out using AmpureXP beads. The libraries were validated using an Agilent Bioanalyser using DNA HS chip. The libraries were normalised, pooled and sequenced on Illumina MiSeq (Illumina Inc., USA) platform at 2 x300 bp length. The whole genome sequencing was performed by sequencing of 7.38 Gb with 73,889,924 paired end reads from paired end library, and 1.15 Gb with 3,851,788 reads from mate pair library generated from Illumina HiSeq2500 and Illumina MiSeq, respectively. The sequences were assembled using various assemblers like ABySS, MaSuRCA, Velvet, SOAPdenovo2, and ALLPATHS-LG. The assembly generated by MaSuRCA (9) algorithm was observed superior over other algorithms and hence used for scaffolding using SSPACE. Assembled draft genome sequence of S. graminicola pathotype 1 was 299,901,251 bp long, with a 47.2 % GC content consisting of 26,786 scaffolds with N50 of 17,909 bp with longest scaffold size of 238,843 bp. The overall coverage was 40X. The draft genome sequence was used for gene prediction using AUGUSTUS. The completeness of the assembly was investigated using CEGMA and revealed 92.74% proteins completely present and 95.56% proteins partially present, while BUSCO fungal dataset indicated 64.9% complete, 12.4% fragmented, 22.7% missing out of 290 BUSCO groups. A total of 52,285 predicted genes were annotated using BLASTX and 38,120 genes were observed with significant BLASTX match. Repetitive element analysis in the assembly revealed 8,196 simple repeats, 1,058 low complexity repeats and 5,562 dinucleotide to hexanucleotide microsatellite repeats.publishersversionPeer reviewe