We present a method for solving the Einstein-Maxwell equations in a five dimensional, asymptotically flat, black hole spacetime with three commuting Killing vector fields. In particular, we show that by reducing the dimension of the Einstein-Maxwell equations in a Kaluza-Klein like manner we can determine the components of the metric and vector potential which lie in the direction of the Killing vector fields. These components are determined by nine scalar fields each of which satisfy a partial differential equation in two variables. These equations take the form of an elliptic operator set equal to a nonlinear source. We find evidence that particular combinations of these fields satisfy Dirichlet boundary conditions, and are well suited to numerical solution using Green functions. Using this method we generate numerical solutions to the 4+1 Einstein-Maxwell equations corresponding to charged generalizations of the Myers-Perry solution. We also discover symmetry relations among the scalar equations which constrain their functional forms and posit the existence of two rigidity-theorem-like relations for electrovac spacetimes and sketch how their use generalizes our method to N+1 dimensions.

Biomechanical properties are key to many cellular functions such as cell division and cell motility and thus are crucial in the development and understanding of several diseases, for instance cancer. The mechanics of the cellular cytoskeleton have been extensively characterized in cells and artificial systems. The rigidity of the plasma membrane, with the exception of red blood cells, is unknown and membrane rigidity measurements only exist for vesicles composed of a few synthetic lipids. In this study, thermal fluctuations of giant plasma membrane vesicles (GPMVs) directly derived from the plasma membranes of primary breast and cervical cells, as well as breast cell lines, are analyzed. Cell blebs or GPMVs were studied via thermal membrane fluctuations and mass spectrometry. It will be shown that cancer cell membranes are significantly softer than their non-malignant counterparts. This can be attributed to a loss of fluid raft forming lipids in malignant cells. These results indicate that the reduction of membrane rigidity promotes aggressive blebbing motion in invasive cancer cells.

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The impact that economic crises have on firms is profound. Such events affect the extent to which firms invest in innovation. This exploratory study aims to investigate to what extentfirms emphasize exploratory and exploitative innovation as a result of economic crises. The study further aims to examine the presence of a rigid or risk-seeking response, in terms of innovation, as a result of the crisis. Through analysis of the contents of the CEOs’ letters to theshareholders, I captured the firms’ emphasis on exploratory and exploitative innovation in a sample of 14 large Swedish firms, three years before and after the crisis and examined the presence of a rigid or risk-seeking response, by comparing both periods. The findings indicate a short-term rigid response as well as no indication of a risk-seeking response. The study contributes to the body of knowledge about how economic crises impact the firms’ emphasis on investing in innovation, a field lacking a consensus among authors.

Rigidity theory deals in problems of the following form: given a structure defined by geometric constraints on a set of objects, what information about its geometric behavior is implied by the underlying combinatorial structure. The most well-studied class of structures is the bar-joint framework, which is made of fixed-length bars connected by universal joints with full rotational degrees of freedom; the allowed motions preserve the lengths and connectivity of the bars, and a framework is rigid if the only allowed motions are trivial motions of Euclidean space. A remarkable theorem of Maxwell-Laman says that rigidity of generic bar-joint frameworks depends only on the graph that has as its edges the bars and as its vertices the joints. We generalize the "degree of freedom counts that appear in the Maxwell-Laman theorem to the very general setting of (k,l)-sparse and (k,l)-graded sparse hypergraphs. We characterize these in terms of their graph-graph theoretic and matroidal properties. For the fundamental algorithmic problems Decision, Extraction, Components, and Decomposition, we give efficient, implementable pebble game algorithms for all the (k,l)-sparse and (k,l)-graded-sparse families of hypergraphs we study. We then prove that all the matroids arising from (k,l)-sparse are linearly representable by matrices with a certain "natural" structure that captures the incidence structure of the hypergraph and the sparsity parameters k and l. Building on the combinatorial and linear theory discussed above, we introduce a new rigidity model: slider-pinning rigidity. This is an elaboration of the planar bar-joint model to include sliders, which constrain a vertex to move on a specific line. We prove the analogue of the Maxwell-Laman Theorem for slider pinning, using, as a lemma, a new proof of Whiteley's Parallel Redrawing Theorem. We conclude by studying the emergence of non-trivial rigid substructures in generic planar frameworks given by Erdos-Renyi random graphs. We prove that there is a sharp threshold for such substructures to emerge, and that, when they do, they are all linear size. This is consistent with experimental and simulation-based work done in the physics community on the formation of certain glasses.

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This dissertation examines the implications of sticky rents on the measurement of owner-occupied housing in the Consumer Price Index (CPI). I argue that marginal and not average rents are the most theoretically justified measurement of owners' equivalent rent (OER), and that the current measurement of rental inflation using average rents is methodologically incorrect. I then discuss the literature on sticky rents and tenure discounts and present a theoretical model showing the implications of sticky rents for aggregate measures of inflation. Then I use two new data sources to construct marginal rent measures to compare to average rent measures. The results show that marginal rents reflect market turning points sooner, and show a larger post- housing bubble decline in rents. In addition, marginal rents are shown to forecast overall inflation better than average rents. Finally, the implications of these results for policy are considered using the Taylor Rule for optimal monetary policy. The results present suggestive evidence that the impacts of switching to marginal rents may be large enough to significantly impact monetary policy and allow the Federal Reserve to be more responsive to both the boom and bust of housing bubbles. / Economics

In this paper we study local rigidity of actions of simply connected Lie groups. In particular, we apply the Nash-Moser inverse function theorem to give sufficient conditions for the action of a simply connected Lie group to be locally rigid. Let $G$ be a Lie group, $H < G$ a simply connected subgroup and $\Gamma < G$ a cocompact lattice. We apply the result for general actions of simply connected groups to obtain sufficient conditions for the action of $H$ on $\Gamma\backslash G$ by right translations to be locally rigid. We also discuss some possible applications of this sufficient condition / I den här texten så studerar vi lokal rigiditet av gruppverkan av enkelt sammanhängande Liegrupper. Mer specifikt, vi applicerar Nash-Mosers inversa funktionssats för att ge tillräckliga villkor för att en gruppverkan av en enkelt sammanhängande grupp ska vara lokalt rigid. Låt $G$ vara en Lie grupp, $H < G$ en enkelt sammanhängande delgrupp och $\Gamma < G$ ett kokompakt gitter. Vi applicerar resultatet för generella gruppverkan av enkelt sammanhängande grupper för att få tillräckliga villkor för att verkan av $H$ på $\Gamma\backslash G$ med translationer ska vara lokalt rigid. Vi diskuterar också några möjliga tillämpningar av det tillräckliga villkoret.