No description available.

No description available.

Mathematics is the science and study of quality, structure, space, and change. It seeks out patterns, formulates new conjectures, and establishes the truth by rigorous deduction from appropriately chosen axioms and definitions. The study of mathematics makes a person better at solving problems. It gives someone skills that (s)he can use across other subjects and apply in many different job roles. In the modern world, builders use mathematics every day to do their work, since construction workers add, subtract, divide, multiply, and work with fractions. It is obvious that mathematics is a major contributor to many areas of study. For this reason, retrieving, ranking, and recommending Math answers, which is an application of Math information retrieval (IR), deserves attention and recognition, since a reliable recommender system helps users find the relevant answers to Math questions and benefits all Math learners whenever they need help solve a Math problem, regardless of the time and place. Such a recommender system can enhance the learning experience and enrich the knowledge in Math of its users. We have developed MaRec, a recommender system that retrieves and ranks Math answers based on their textual content and embedded formulas in answering a Math question. MaRec (i) applies KL-divergence to rank the textual content of a potential answer A with respect to the textual content of a Math question Q, and (ii) together with the representation of the Math formulas in Q and A as XML trees determines their subtree matching scores in ranking A as an answer to Q. The design of MaRec is simple, since it does not require the training and test process mandated by machine learning-based Math IR systems, which is tedious to set up and time consuming to train the models. Conducted empirical studies show that MaRec significantly outperforms (i) three existing state-of-the-art MathIR systems based on an offline evaluation, and (ii) a top-of-the-line machine learning system based on an online performance analysis.

The genus Rhodotorula includes basidiomycetous oleaginous yeast species. Rhodotorula babjevae can produce compounds of biotechnological interest such as lipids, carotenoids, and biosurfactants from low value substrates such as lignocellulose hydrolysate. High-quality genome assemblies are needed to develop genetic tools and to understand fungal evolution and genetics. Here, we combined short- and long-read sequencing to resolve the genomes of two R. babjevae strains, CBS 7808 (type strain) and DBVPG 8058, at chromosomal level. Both genomes are 21 Mbp in size and have a GC content of 68.2%. Allele frequency analysis indicates that both strains are tetraploid. The genomes consist of a maximum of 21 chromosomes with a size of 0.4 to 2.4 Mbp. In both assemblies, the mitochondrial genome was recovered in a single contig, that shared 97% pairwise identity. Pairwise identity between most chromosomes ranges from 82 to 87%. We also found indications for strain-specific extrachromosomal endogenous DNA. A total of 7591 and 7481 protein-coding genes were annotated in CBS 7808 and DBVPG 8058, respectively. CBS 7808 accumulated a higher number of tandem duplications than DBVPG 8058. We identified large translocation events between putative chromosomes. Genome divergence values between the two strains indicate that they may belong to different species.

Analysis of rhesus monkey alphoid DNA suggests that it arose by tandem duplication of an ancestral monomer unit followed by independent variation within two adjacent monomers (one becoming more divergent than the other) before their amplification as a dimer unit to produce tandem arrays. The rhesus monkey alphoid DNA is a tandemly repeated, 343-bp dimer; the consensus dimer is over 98% homologous to the alphoid dimers reported for baboon and bonnet monkey, 81% homologous to the African green monkey alpha monomer, and less than 70% homologous to the more divergent human alphoid DNAs. The consensus dimer consists of two wings (I and II, 172 and 171 bp, respectively) that are only 70% homologous to each other, but share seven regions of exact homology. These same regions are highly conserved among the consensus sequences of the other cercopithecid alphoid DNAs. The three alpha-protein binding sites reported for African green monkey alpha DNA by F. Strauss and A. Varshavsky (Cell 37: 889-901, 1984) occur in wings I and II, but with one site altered in wing I. Two cloned dimer segments are 98% homologous to the consensus, each containing 8 single-base-pair differences within the 343-bp segment. Surprisingly, 37% of these differences occur in regions that are evolutionarily conserved in the alphoid consensus sequences, including the alpha-protein binding sites. Sequence variation in this highly repetitive DNA family may produce unique nucleosomal architectures for different members of an alphoid array. These unique architectures may modulate the evolution of these repetitive DNAs and may produce unique centromeric characteristics in primate chromosomes.

This study focuses on a secondary contact zone between two sister species of woodrat, Neotoma fuscipes (dusky-footed woodrat) and N. macrotis (big-eared woodrat). Along the Nacimiento River, on the border of southern Monterey and northern San Luis Obispo counties, the ranges of these sister species of woodrats meet and overlap forming a secondary contact zone. The zone of secondary contact is estimated to include a 500-meter (~1,650 linear feet) portion of the Nacimiento River riparian corridor. This research examines quantifiable morphological change that is likely associated with heightened inter-specific competition within the contact zone. When in sympatry the sister species may compete for resources indirectly through exploitative competition, or directly through contest competition, or through a combination of these two processes. The prediction that heightened competition has resulted in distinctive morphological character shifts between allopatric and sympatric populations was tested my examining size and shape of adult woodrats along a 20-kilometer transect. It was confirmed that adults woodrats of the two sister taxa are morphologically distinct (N = 602) and that the phallus morphology was indeed a reliable means to identify adult male woodrats as to species (p < 0.0001, N = 331). A two model approach was used to examine convergence and divergence in size and shape of woodrats across the transect. Neotoma fuscipes exhibited a statistically significant divergerence from N. macrotis with regard to breadth of rostrum (p < 0.0001, N = 414) in a region of sympatry along the Nacimiento River. Based on the results on one statistical model, N. macrotis exhibited a statistically significant convergence with regard to body-size (p = 0.0240, N = 587) and length of hind foot (p < 0.0001, N = 563) towards those of N. fuscipes between zones of sympatry and allopatry. Alternatively, based on the results of a second statistical model that accounted for environmental variation within the system both species exhibited a statistically significant divergence with regard to body-size (p = 0.0054, N = 587) and towards that of N. fuscipes between zones of sympatry and allopatry. Also, N. macrotis exhibited a statistically significant convergence with regard to length of ear (p = 0.0022, N = 563) towards that of N. fuscipes. Based on the results of both models, detectable re-patterning of size-independent traits was observed to varying degrees. The morphological character shifts between sympatric populations and allopatric populations of woodrats suggest that ecological interactions between the species are occuring. Specifically, across the contact zone, patterns of variation in body-size and other morphological character traits are consistent with expectations of a combination of contest and exploitative competition.

Ammomanes cinctura (Bar-tailed Lark) is a lark species with a wide distribution in the Palearctic. One of its subspecies, A. c. arenicolor, has a wide range across northern Africa, within which it shows very minor morphological variation but deep divergence in the mitochondrial cytochrome b locus between two geographically widely separated populations. There are two additional allopatric subspecies, A. c. cinctura (Cape Verde Islands) and A. c. zarudnyi (Iran to Pakistan), which differ slightly more in morphology. The genomic population structure, evolutionary history, and taxonomic status of the different populations within this species remain unclear. I applied an integrative approach, using genomic single nucleotide polymorphisms (SNPs), mtDNA and morphological data, to investigate the evolutionary divergence within Ammomanes cinctura. I acquired whole-genome sequence data from twelve individuals from Morocco (n=2), Saudi Arabia (n=7), and Iran (n=3), and performed phylogenetic and population structure analyses. Mitochondrial genomes were assembled and cytochrome b was extracted for phylogeny. Biometric measurements and quantified plumage analysis were conducted on museum specimens of all three subspecies. According to the mitochondrial data, the samples from Saudi Arabia and Iran form a clade that is deeply diverged (5.94 Mya, 95%HPD 3.15–8.95 Mya) from a clade comprising the samples from Morocco and Cape Verde Islands. In contrast, the nuclear SNPs recovered a very shallow divergence (0.095 Mya, 95%HPD 0.04-0.16 Mya) and weak population structure between the samples from Morocco vs. Saudi Arabia–Iran. Morphological results indicated that zarudnyi is slightly differentiated from the other two subspecies, with a larger body size, and the three subspecies are slightly divergent in plumage. The close similarity between Moroccan and Saudi Arabian birds in morphology was also confirmed, in conflict with the molecular data – highlighting the problem with trinomials in this case. The results suggest that the deep divergence in mitochondrial DNA is due to a complex evolutionary history.

In dieser Dissertation analysieren wir drei Aspekte von Konforme Feldtheorien (CFTs). Erstens betrachten wir Korrelationsfunktionen von sekundären Zuständen (SZ) in zweidimensionalen CFTs. Wir diskutieren eine rekursive Formel zu ihrer Berechnung und erstellen eine Computerimplementierung dieser Formel. Damit können wir jede Korrelationsfunktion von SZ des Vakuums erhalten und für Nicht-Vakuum-SZ den Korrelator als Differentialoperator, der auf den jeweiligen primären Korrelator wirkt, ausdrücken. Mit diesem Code untersuchen wir dann einige Verschränkungs- und Unterscheidbarkeitsmaße zwischen SZ, i.e. die Rényi-Entropie, den Spurquadratabstand und die Sandwich-Rényi-Divergenz. Mit unseren Ergebnissen können wir die Rényi Quanten-Null-Energie-Bedingung testen und stellen neue Werkzeuge zur Analyse der holographischen Beschreibung von SZ bereit. Zweitens untersuchen wir vierdimensionale Weyl-Fermionen auf verschiedenen Hintergründen. Unser Interesse gilt ihrer Spuranomalie, und der Frage, ob die Pontryagin-Dichte auftritt. Deshalb berechnen wir die Anomalien von Dirac-Fermionen, die an vektorielle und axiale Eichfelder gekoppelt sind, und dann auf einem metrisch-axialen Tensor Hintergrund. Geeignete Grenzwerte der Hintergründe erlauben es dann, die Anomalien von Weyl-Fermionen, die an Eichfelder gekoppelt sind, und in einer gekrümmten Raumzeit zu berechnen. Wir bestätigen das Fehlen der Pontryagin-Dichte in den Spuranomalien. Drittens liefern wir die holographische Beschreibung einer vierdimensionalen CFT mit einem irrelevanten Operator. Wenn der Operator eine ganzzahlige konforme Dimension hat, modifiziert sein Vorhandensein in der CFT die Weyl-Transformation der Metrik, was wiederum die Spuranomalie ändert. Unter Ausnutzung der Äquivalenz zwischen Diffeomorphismen im Inneren und Weyl-Transformationen auf dem Rand, berechnen wir diese Modifikationen mithilfe der dualen Gravitationstheorie. Unsere Ergebnisse repräsentieren einen weiteren Test der AdS/CFT-Korrespondenz. / Conformal field theories (CFTs) are amongst the most studied field theories and they offer a remarkable playground in modern theoretical physics. In this thesis we analyse three aspects of CFTs in different dimensions. First, we consider correlation functions of descendant states in two-dimensional CFTs. We discuss a recursive formula to calculate them and provide a computer implementation of it. This allows us to obtain any correlation function of vacuum descendants, and for non-vacuum descendants to express the correlator as a differential operator acting on the respective primary correlator. With this code, we study some entanglement and distinguishability measures between descendant states, i.e. the Rényi entropy, trace square distance and sandwiched Rényi divergence. With our results we can test the Rényi Quantum Null Energy Condition and provide new tools to analyse the holographic description of descendant states. Second, we study four-dimensional Weyl fermions on different backgrounds. Our interest is in their trace anomaly, where the Pontryagin density has been claimed to appear. To ascertain this possibility, we compute the anomalies of Dirac fermions coupled to vector and axial non-abelian gauge fields and then in a metric-axial-tensor background. Appropriate limits of the backgrounds allow to recover the anomalies of Weyl fermions coupled to non-abelian gauge fields and in a curved spacetime. In both cases we confirm the absence of the Pontryagin density in the trace anomalies. Third, we provide the holographic description of a four-dimensional CFT with an irrelevant operator. When the operator has integer conformal dimension, its presence in the CFT modifies the Weyl transformation of the metric, which in turns modifies the trace anomaly. Exploiting the equivalence between bulk diffeomorphisms and boundary Weyl transformations, we compute these modifications from the dual gravity theory. Our results represent an additional test of the AdS/CFT conjecture.

No description available.

No description available.