Heterogeneous labour and the determination of value

Heterogeneity of labour and its implications for the Marxian theory of value has been one of the most controversial issues in the literature of the Marxist political economy. The adoption of Marx's conjecture about a uniform rate of surplus value leads to a simultaneous determination of the values of common and labour commodities of different types and the uniform rate of surplus value. Determination of these variables can be formally represented as a parametric cigenvalue problem. Morishima's and Bródy's earlier results are analysed and given new interpretations in the light of the suggested procedure. The main questions are addressed in a more general context too. The analysis is extended to the problem of segmented labour market, as well.

Thinking in three dimensions: Exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad

Current reform initiatives recommend that geometry instruction include the study of three-dimensional geometric objects and provide students with opportunities to use spatial skills in problem-solving tasks. Geometer's Sketchpad (GSP) is a dynamic and interactive computer program that enables the user to investigate and explore geometric concepts and manipulate geometric structures. Research using GSP as an instructional tool has focused primarily on teaching and learning two-dimensional geometry. This study explored the effect of a GSP based instructional environment on students' geometric thinking and three-dimensional spatial ability as they used GSP to learn three-dimensional geometry. For 10 weeks, 18 tenth-grade students from an urban school district used GSP to construct and analyze dynamic, two-dimensional representations of three-dimensional objects in a classroom environment that encouraged exploration, discussion, conjecture, and verification. The data were collected primarily from participant observations and clinical interviews and analyzed using qualitative methods of analysis. In addition, pretest and posttest measures of three-dimensional spatial ability and van Hiele level of geometric thinking were obtained. Spatial ability measures were analyzed using standard t-test analysis. ^ The data from this study indicate that GSP is a viable tool to teach students about three-dimensional geometric objects. A comparison of students' pretest and posttest van Hiele levels showed an improvement in geometric thinking, especially for students on lower levels of the van Hiele theory. Evidence at the p < .05 level indicated that students' spatial ability improved significantly. Specifically, the GSP dynamic, visual environment supported students' visualization and reasoning processes as students attempted to solve challenging tasks about three-dimensional geometric objects. The GSP instructional activities also provided students with an experiential base and an intuitive understanding about three-dimensional objects from which more formal work in geometry could be pursued. This study demonstrates that by designing appropriate GSP based instructional environments, it is possible to help students improve their spatial skills, develop more coherent and accurate intuitions about three-dimensional geometric objects, and progress through the levels of geometric thinking proposed by van Hiele. ^

Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.

Economia criativa e estratégia como prática social: uma abordagem teórico-empírico-conceitual a partir de ambientes criativos de grupos musicais

This study seeks to identify how creative environments of musical groups are configured in the Strategy as Practice perspective as theoretical, empirical and conceptual models. It develops within the theoretical framework, discussions on the context of the Creative Economy, Creative Industries, creative environment, organizational paradigm of Creative Economy, music as a creative environment and business, design and dynamics of Strategy as Practice and conjecture about the contextualism and other epistemological currents. The study is shaped as an exploratory and descriptive research, utilizing the qualitative method and being characterized as a Grounded Theory. A total of four musical groups of different styles, markets and areas of operation with over ten years of activity were surveyed. The Grounded Theory and simple observation methods were used for both data collection and analysis. The software ATLAS.ti. was used to help with the analysis. The research shows that the bands perceive the specialized expertise in the virtual social media as a strategic differentiator. It also shows that the groups nourish individuation and the differentiation in their relationship with the individual. Finally, it validates that these organizations get teams involved and value the dynamic design of their routines in strategic decision making, paying attention to a strategic social bias. Strategy and Creative Practice is the main category that emerged from the data. This category is explained through the three aforementioned results. It shows that organizations that are part of the Creative Economy perform simultaneously and dynamically creative and strategic making at both artistic and managerial levels.The theory created is validated by the principles of degree of coherence, functionality, relevance, flexibility, density and integration, and it is inserted in the contextualism principle, which points the knowledge as related to the context in which it is placed and discussed.

Treeline dynamics in Siberia under changing climates as inferred from an individual-based model for Larix, supplementary material

Siberian boreal forests are expected to expand northwards in the course of global warming. However, processes of the treeline ecotone transition, as well astiming and related climate feedbacks are still not understood. Here, we present 'Larix Vegetation Simulator' LAVESI, an individual-based spatially-explicit model that can simulate Larix gmelinii (RUPR.) RUPR. stand dynamics in an attempt to improve our understanding about past and future treeline movements under changing climates. The relevant processes (growth, seed production and dispersal, establishment and mortality) are incorporated and adjusted to observation data mainly gained from the literature. Results of a local sensitivity analysis support the robustness of the model's parameterization by giving relatively small sensitivity values. We tested the model by simulating tree stands under modern climate across the whole Taymyr Peninsula, north-central Siberia (c. 64-80° N; 92-119° E). We find tree densities similar to observed forests in the northern to mid-treeline areas, but densities are overestimated in the southern parts of the simulated region. Finally, from a temperature-forcing experiment, we detect that the responses of tree stands lag the hypothetical warming by several decades, until the end of 21st century. With our simulation experiments we demonstrate that the newly-developed model captures the dynamics of the Siberian latitudinal treeline.

Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Optimal 5-step nilpotent quadratic algebras

By the Golod–Shafarevich theorem, an associative algebra $R$ given by $n$ generators and $<n^2/3$ homogeneous quadratic relations is not 5-step nilpotent. We prove that this estimate is optimal. Namely, we show that for every positive integer $n$, there is an algebra $R$ given by $n$ generators and $\lceil n^2/3\rceil$ homogeneous quadratic relations such that $R$ is 5-step nilpotent.

On Pauli pairs

The state of a system in classical mechanics can be uniquely reconstructed if we know the positions and the momenta of all its parts. In 1958 Pauli has conjectured that the same holds for quantum mechanical systems. The conjecture turned out to be wrong. In this paper we provide a new set of examples of Pauli pairs, being the pairs of quantum states indistinguishable by measuring the spatial location and momentum. In particular, we construct a new set of spatially localized Pauli pairs.

Two problems from the Polishchuk and Positselski book on Quadratic algebras

In the book ’Quadratic algebras’ by Polishchuk and Positselski [23] algebras with a small number of generators (n = 2, 3) are considered. For some number r of relations possible Hilbert series are listed, and those appearing as series of Koszul algebras are specified. The first case, where it was not possible to do, namely the case of three generators n = 3 and six relations r = 6 is formulated as an open problem. We give here a complete answer to this question, namely for quadratic algebras with dimA_1 = dimA_2 = 3, we list all possible Hilbert series, and find out which of them can come from Koszul algebras, and which can not. As a consequence of this classification, we found an algebra, which serves as a counterexample to another problem from the same book [23] (Chapter 7, Sec. 1, Conjecture 2), saying that Koszul algebra of finite global homological dimension d has dimA_1 > d. Namely, the 3-generated algebra A given by relations xx + yx = xz = zy = 0 is Koszul and its Koszul dual algebra A^! has Hilbert series of degree 4: HA! (t) = 1 + 3t + 3t^2 + 2t^3 + t^4, hence A has global homological dimension 4.

Undersampled Critical Branching Processes on Small-World and Random Networks Fail to Reproduce the Statistics of Spike Avalanches

The power-law size distributions obtained experimentally for neuronal avalanches are an important evidence of criticality in the brain. This evidence is supported by the fact that a critical branching process exhibits the same exponent t~3=2. Models at criticality have been employed to mimic avalanche propagation and explain the statistics observed experimentally. However, a crucial aspect of neuronal recordings has been almost completely neglected in the models: undersampling. While in a typical multielectrode array hundreds of neurons are recorded, in the same area of neuronal tissue tens of thousands of neurons can be found. Here we investigate the consequences of undersampling in models with three different topologies (two-dimensional, small-world and random network) and three different dynamical regimes (subcritical, critical and supercritical). We found that undersampling modifies avalanche size distributions, extinguishing the power laws observed in critical systems. Distributions from subcritical systems are also modified, but the shape of the undersampled distributions is more similar to that of a fully sampled system. Undersampled supercritical systems can recover the general characteristics of the fully sampled version, provided that enough neurons are measured. Undersampling in two-dimensional and small-world networks leads to similar effects, while the random network is insensitive to sampling density due to the lack of a well-defined neighborhood. We conjecture that neuronal avalanches recorded from local field potentials avoid undersampling effects due to the nature of this signal, but the same does not hold for spike avalanches. We conclude that undersampled branching-process-like models in these topologies fail to reproduce the statistics of spike avalanches.

On f-vectors of polytopes and matroids

Thesis (Ph.D.)--University of Washington, 2016-08

Phylum-wide transcriptome analysis of oogenesis and early embryogenesis in selected nematode species

Oogenesis is a prerequisite for embryogenesis in Metazoa. During both biological processes important decisions must be made to form the embryo and hence ensure the next generation: (1) Maternal gene products (mRNAs, proteins and nutrients) must be supplied to the embryo. (2) Polarity must be established and axes must be specified. While incorporation of maternal gene products occurs during oogenesis, the time point of polarity establishment and axis specification varies among species, as it is accomplished either prior, during, or after fertilisation. But not only the time point when these events take place varies among species but also the underlying mechanisms by which they are triggered. For the nematode model Caenorhabditis elegans the underlying pathways and gene regulatory networks (GRNs) are well understood. It is known that there the sperm entry point initiates a primary polarity in the 1-celled egg and with it the establishment of the anteroposterior axis. However, studies of other nematodes demonstrated that polarity establishment can be independent of sperm entry (Goldstein et al., 1998; Lahl et al., 2006) and that cleavage patterns, symmetry formation and cell specification also differ from C. elegans. In contrast to the studied Chromadorea (more derived nematodes including C. elegans), embryos of some marine Enoplea (more basal representatives) even show no discernible early polarity and blastomeres can adopt variable cell fates (Voronov and Panchin 1998). The underlying pathways controlling the obviously variant embryonic processes in non-Caenorhabditis nematodes are essentially unknown. In this thesis I addressed this issue by performing a detailed unbiased comparative transcriptome analysis based on microarrays and RNA sequencing of selected developmental stages in a variety of nematodes from different phylogenetic branches with C. elegans as a reference system and a nematomorph as an outgroup representative. In addition, I made use of available genomic data to determine the presence or absence of genes for which no expression had been detected. In particular, I focussed on components of selected pathways or GRNs which are known to play essential roles during C. elegans development and/or other invertebrate or vertebrate model systems. Oogenesis must be regulated differently in non-Caenorhabditis nematodes, as crucial controlling components of Wnt and sex determination signaling are absent in these species. In this respect, I identified female-specific expression of potential polarity associated genes during gonad development and oogenesis in the Enoplean nematode Romanomermis culicivorax. I could show that known downstream components of the polarity complexes PAR-3/-6/PKC-3 and PAR-1/-2 are absent in non-Caenorhabditis species. Even PAR-2 as part of the polarity complex does not exist in these nematodes. Instead, transcriptomes of nematodes (including C. elegans), show expression of other polarity-associated complexes such as the Lgl (Lethal giant larvae) complex. This result could pose an alternative route for nematodes and nematomorphs to initiate polarity during early embryogenesis. I could show that crucial pathways of axis specification, such as Wnt and BMP are very different in C. elegans compared to other nematodes. In the former, Wnt signaling, for instance, is mediated by four paralogous beta-catenins, while other Chromadorea have fewer and Enoplea only one beta-catenin. The transcriptomes of R. culicivorax and the nematomorph show that regulators of BMP (e.g. Chordin), are specifically expressed during early embryogenesis only in Enoplea and the close outgroup of nematomorphs. In conclusion, my results demonstrate that the molecular machinery controlling oogenesis and embryogenesis in nematodes is unexpectedly variable and C. elegans cannot be taken as a general model for nematode development. Under this perspective, Enoplean nematodes show more similarities with outgroups than with C. elegans. It appears that certain pathway components were lost or gained during evolution and others adopted new functions. Based on my findings I can conjecture, which pathway components may be ancestral and which were newly acquired in the course of nematode evolution.

Some results on orbifold quotients and related objects

The quotient of a finite-dimensional Euclidean space by a finite linear group inherits different structures from the initial space, e.g. a topology, a metric and a piecewise linear structure. The question when such a quotient is a manifold leads to the study of finite groups generated by reflections and rotations, i.e. by orthogonal transformations whose fixed point subspace has codimension one or two. We classify such groups and thereby complete earlier results by M. A. Mikhaîlova from the 70s and 80s. Moreover, we show that a finite group is generated by reflections and) rotations if and only if the corresponding quotient is a Lipschitz-, or equivalently, a piecewise linear manifold (with boundary). For the proof of this statement we show in addition that each piecewise linear manifold of dimension up to four on which a finite group acts by piecewise linear homeomorphisms admits a compatible smooth structure with respect to which the group acts smoothly. This solves a challenge by Thurston and confirms a conjecture by Kwasik and Lee. In the topological category a counterexample to the above mentioned characterization is given by the binary icosahedral group. We show that this is the only counterexample up to products. In particular, we answer the question by Davis of when the underlying space of an orbifold is a topological manifold. As a corollary of our results we generalize a fixed point theorem by Steinberg on unitary reflection groups to finite groups generated by reflections and rotations. As an application thereof we answer a question by Petrunin on quotients of spheres.

Integrability for Relativistic Spin Networks

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.

A Lorentzian Signature Model for Quantum General Relativity

We give a relativistic spin network model for quantum gravity based on the Lorentz group and its q-deformation, the Quantum Lorentz Algebra. We propose a combinatorial model for the path integral given by an integral over suitable representations of this algebra. This generalises the state sum models for the case of the four-dimensional rotation group previously studied in gr-qc/9709028. As a technical tool, formulae for the evaluation of relativistic spin networks for the Lorentz group are developed, with some simple examples which show that the evaluation is finite in interesting cases. We conjecture that the `10J' symbol needed in our model has a finite value.