Spaces of matrices of fixed rank. II

AbstractWhen min{m, n} = k + 1, the exact value of l(k, m, n), the maximum dimension of all possible linear spaces of rank k matrices of order m × n, is known. The situation when min l(k, m, n) ⩾ k + 2 is not clear. Partial results are obtained for l(k, k + 2, k + 2) in this paper

LINKING PREVIOUS EXPERIENCES TO BEHAVIOR AND HEALTH IN THE HONEY BEE (\u3ci\u3eApis mellifera\u3c/i\u3e)

An organism’s ability to respond to changing conditions can be vital to its success. Indeed, plasticity is a common feature of living organisms. Much of the research in this area, though, has focused on effects caused by environmental conditions. What has received relatively less attention is how social experiences and broader features of an organism’s social environment can lead to long-lasting changes in health and behavior. This knowledge gap exists despite the well-documented existence of health and behavioral effects after social interactions in certain taxa such as humans. Social insects such as honey bees provide an excellent opportunity to better understand this phenomenon due to their well-characterized behavioral repertoire, complex social dynamics, and experimental tractability in natural and semi-natural settings. This project examines multiple aspects of honey bee behavior and health to determine how they are affected by a bee’s previous experiences. Additionally, this project aims to uncover how elements of the social environment (such as colony-level aggression) lead to different outcomes in adult behavior, physiology, and health in these insects. I first documented the existence of high colony-level variation in the nutritional profile of “worker jelly.” Worker jelly is a nutritional secretion that is synthesized by adult nurse bees and comprises the entirety of the nutritional resources available to a honey bee larva, making it a critical feature of the early-life development period for bees. Next, I examined the social interaction element of nurse bees inspecting and feeding larvae. I determined that this vital interaction can be affected by social pheromones such as the honey bee alarm pheromone. This effect was dependent on the colony-level aggressive social environment, however, despite these nurses not being specialized for aggressive nest defense. I then followed up on the previous results by using electrophysiology to determine that colony-level aggression differentially affects the peripheral detection of some social pheromones in nurses but not in bees of a typically more aggressive task specialization, foragers. Finally, I turned the lens to the adult social interaction of allogrooming. Allogrooming is a key component of a honey bee colony’s health-promoting “social immunity.” I tested how an acute allogrooming event affects the expression of key immune genes from multiple pathways as well as deeply conserved genes implicated in social responsiveness across taxa. This work demonstrates how early life experiences and social interactions can affect the health and behavior of a highly social organism. Additionally, given the recent challenges faced by these important pollinators, this research provides key foundational knowledge on the importance of social factors in maintaining the overall health and vitality of honey bees and honey bee colonies

Geometry of lines and degeneracy loci of morphisms of vector bundles

Corrado Segre played a leading role in the foundation of line geometry. We survey some recent results on degeneracy loci of morphisms of vector bundles where he still is of profound inspiration.Comment: 10 pages. To appear in the proceedings of the conference "Homage to Corrado Segre

Insects Provide Unique Systems to Investigate How Early-Life Experience Alters the Brain and Behavior

Early-life experiences have strong and long-lasting consequences for behavior in a surprising diversity of animals. Determining which environmental inputs cause behavioral change, how this information becomes neurobiologically encoded, and the functional consequences of these changes remain fundamental puzzles relevant to diverse fields from evolutionary biology to the health sciences. Here we explore how insects provide unique opportunities for comparative study of developmental behavioral plasticity. Insects have sophisticated behavior and cognitive abilities, and they are frequently studied in their natural environments, which provides an ecological and adaptive perspective that is often more limited in lab-based vertebrate models. A range of cues, from relatively simple cues like temperature to complex social information, influence insect behavior. This variety provides experimentally tractable opportunities to study diverse neural plasticity mechanisms. Insects also have a wide range of neurodevelopmental trajectories while sharing many developmental plasticity mechanisms with vertebrates. In addition, some insects retain only subsets of their juvenile neuronal population in adulthood, narrowing the targets for detailed study of cellular plasticity mechanisms. Insects and vertebrates share many of the same knowledge gaps pertaining to developmental behavioral plasticity. Combined with the extensive study of insect behavior under natural conditions and their experimental tractability, insect systems may be uniquely qualified to address some of the biggest unanswered questions in this field

On the dimension of subspaces with bounded Schmidt rank

We consider the question of how large a subspace of a given bipartite quantum system can be when the subspace contains only highly entangled states. This is motivated in part by results of Hayden et al., which show that in large d x d--dimensional systems there exist random subspaces of dimension almost d^2, all of whose states have entropy of entanglement at least log d - O(1). It is also related to results due to Parthasarathy on the dimension of completely entangled subspaces, which have connections with the construction of unextendible product bases. Here we take as entanglement measure the Schmidt rank, and determine, for every pair of local dimensions dA and dB, and every r, the largest dimension of a subspace consisting only of entangled states of Schmidt rank r or larger. This exact answer is a significant improvement on the best bounds that can be obtained using random subspace techniques. We also determine the converse: the largest dimension of a subspace with an upper bound on the Schmidt rank. Finally, we discuss the question of subspaces containing only states with Schmidt equal to r.Comment: 4 pages, REVTeX4 forma

Automorphism groups of Grassmann codes

We use a theorem of Chow (1949) on line-preserving bijections of Grassmannians to determine the automorphism group of Grassmann codes. Further, we analyze the automorphisms of the big cell of a Grassmannian and then use it to settle an open question of Beelen et al. (2010) concerning the permutation automorphism groups of affine Grassmann codes. Finally, we prove an analogue of Chow's theorem for the case of Schubert divisors in Grassmannians and then use it to determine the automorphism group of linear codes associated to such Schubert divisors. In the course of this work, we also give an alternative short proof of MacWilliams theorem concerning the equivalence of linear codes and a characterization of maximal linear subspaces of Schubert divisors in Grassmannians.Comment: revised versio

The Peaceful Atom Comes to Campus

Youthful idealism, institutional ambition, and Cold War sensibilities all helped shape the Michigan Memorial–Phoenix Project, the University of Michigan’s tribute to fallen World War II soldiers.</jats:p

Oncogenic Ras activation of Raf/mitogen-activated protein kinase-independent pathways is sufficient to cause tumorigenic transformation

Substantial evidence supports a critical role for the activation of the Raf-1/MEK/mitogen-activated protein kinase pathway in oncogenic Ras-mediated transformation. For example, dominant negative mutants of Raf-1, MEK, and mitogen-activated protein kinase all inhibit Ras transformation. Furthermore, the observation that plasma membrane-localized Raf-1 exhibits the same transforming potency as oncogenic Ras suggests that Raf-1 activation alone is sufficient to mediate full Ras transforming activity. However, the recent identification of other candidate Ras effectors (e.g., RalGDS and phosphatidylinositol-3 kinase) suggests that activation of other downstream effector-mediated signaling pathways may also mediate Ras transforming activity. In support of this, two H-Ras effector domain mutants, H-Ras(12V, 37G) and H-Ras(12V, 40C), which are defective for Raf binding and activation, induced potent tumorigenic transformation of some strains of NIH 3T3 fibroblasts. These Raf-binding defective mutants of H-Ras induced a transformed morphology that was indistinguishable from that induced by activated members of Rho family proteins. Furthermore, the transforming activities of both of these mutants were synergistically enhanced by activated Raf-1 and inhibited by the dominant negative RhoA(19N) mutant, indicating that Ras may cause transformation that occurs via coordinate activation of Raf-dependent and -independent pathways that involves Rho family proteins. Finally, cotransfection of H-Ras(12V, 37G) and H-Ras(12V, 40C) resulted in synergistic cooperation of their focus-forming activities, indicating that Ras activates at least two Raf-independent, Ras effector-mediated signaling events

Characterizing Operations Preserving Separability Measures via Linear Preserver Problems

We use classical results from the theory of linear preserver problems to characterize operators that send the set of pure states with Schmidt rank no greater than k back into itself, extending known results characterizing operators that send separable pure states to separable pure states. We also provide a new proof of an analogous statement in the multipartite setting. We use these results to develop a bipartite version of a classical result about the structure of maps that preserve rank-1 operators and then characterize the isometries for two families of norms that have recently been studied in quantum information theory. We see in particular that for k at least 2 the operator norms induced by states with Schmidt rank k are invariant only under local unitaries, the swap operator and the transpose map. However, in the k = 1 case there is an additional isometry: the partial transpose map.Comment: 16 pages, typos corrected, references added, proof of Theorem 4.3 simplified and clarifie

Rac regulation of transformation, gene expression, and actin organization by multiple, PAK-independent pathways.

Rac1 and RhoA are members of the Rho family of Ras-related proteins and function as regulators of actin cytoskeletal organization, gene expression, and cell cycle progression. Constitutive activation of Rac1 and RhoA causes tumorigenic transformation of NIH 3T3 cells, and their functions may be required for full Ras transformation. The effectors by which Rac1 and RhoA mediate these diverse activities, as well as the interrelationship between these events, remain poorly understood. Rac1 is distinct from RhoA in its ability to bind and activate the p65 PAK serine/threonine kinase, to induce lamellipodia and membrane ruffling, and to activate the c-Jun NH2-terminal kinase (JNK). To assess the role of PAK in Rac1 function, we identified effector domain mutants of Rac1 and Rac1-RhoA chimeric proteins that no longer bound PAK. Surprisingly, PAK binding was dispensable for Rac1-induced transformation and lamellipodium formation, as well as activation of JNK, p38, and serum response factor (SRF). However, the ability of Rac1 to bind to and activate PAK correlated with its ability to stimulate transcription from the cyclin D1 promoter. Furthermore, Rac1 activation of JNK or SRF, or induction of lamellipodia, was neither necessary nor sufficient for Rac1 transforming activity. Finally, the signaling pathways that mediate Rac1 activation of SRF or JNK were distinct from those that mediate Rac1 induction of lamellipodia. Taken together, these observations suggest that Rac1 regulates at least four distinct effector-mediated functions and that multiple pathways may contribute to Rac1-induced cellular transformation