A distance on curves modulo rigid transformations

We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations). Given two curves, the distance between them is defined as the infimum of an energy functional which, roughly speaking, measures the extent to which the jet field of the first curve needs to be rotated to match up with the jet field of the second curve. We show that this energy functional attains a global minimum on the appropriate function space, and we derive a set of first-order ODEs for the minimizer.Comment: 22 pages, 1 figure; final version as published with minor typos correcte

Source-oriented model for air pollutant effects on visibility

A source-oriented model for air pollutant effects on visibility has been developed that can compute light scattering, light extinction, and estimated visual range directly from data on gas phase and primary particle phase air pollutant emissions from sources. The importance of such a model is that it can be used to compute the effect of emission control proposals on visibility-related parameters in advance of the adoption of such control programs. The model has been assembled by embedding several aerosol process modules within the photochemical trajectory model previously developed for aerosol nitrate concentration predictions by Russell et al. [1983] and Russell and Cass [1986]. These modules describe the size distribution and chemical composition of primary particle emissions, the speciation of organic vapor emissions, atmospheric chemical reactions, transport of condensible material between the gas and the particle phases, fog chemistry, dry deposition, and atmospheric light scattering and light absorption. Model predictions have been compared to observed values using 48-hour trajectories arriving at Claremont, California, at each hour of August 28, 1987, during the Southern California Air Quality Study. The predicted fine particle concentration averages 62 μg m^(−3) compared to an observed value of 61 μg m^(−3), while predicted PM_(10) concentrations average 102 μg m^(−3) compared to an observed average of 97 μg m^(−3). The size distribution and chemical composition predictions for elemental carbon, sulfate, and sodium ion agree with observations to within plus or minus a few micrograms per cubic meter, while ammonium and nitrate concentrations are underpredicted by the base case model by 3 to 7 μg m^(−3) on average. Light-scattering coefficient values are calculated from the predicted aerosol size distribution and refractive index, and the model predictions agree with measured values on average to within 19%. The advantages and limitations of the modeling procedure are discussed

Hematopoietic versus Solid Cancers and T Cell Dysfunction: Looking for Similarities and Distinctions

Cancer cells escape, suppress and exploit the host immune system to sustain themselves, and the tumor microenvironment (TME) actively dampens T cell function by various mechanisms. Over the last years, new immunotherapeutic approaches, such as adoptive chimeric antigen receptor (CAR) T cell therapy and immune checkpoint inhibitors, have been successfully applied for refractory malignancies that could only be treated in a palliative manner previously. Engaging the anti-tumor activity of the immune system, including CAR T cell therapy to target the CD19 B cell antigen, proved to be effective in acute lymphocytic leukemia. In low-grade hematopoietic B cell malignancies, such as chronic lymphocytic leukemia, clinical outcomes have been tempered by cancer-induced T cell dysfunction characterized in part by a state of metabolic lethargy. In multiple myeloma, novel antigens such as BCMA and CD38 are being explored for CAR T cells. In solid cancers, T cell-based immunotherapies have been applied successfully to melanoma and lung cancers, whereas application in e.g., breast cancer lags behind and is modestly effective as yet. The main hurdles for CAR T cell immunotherapy in solid tumors are the lack of suitable antigens, anatomical inaccessibility, and T cell anergy due to immunosuppressive TME. Given the wide range of success and failure of immunotherapies in various cancer types, it is crucial to comprehend the underlying similarities and distinctions in T cell dysfunction. Hence, this review aims at comparing selected, distinct B cell-derived versus solid cancer types and at describing means by which malignant cells and TME might dampen T cell anti-tumor activity, with special focus on immunometabolism. Drawing a meaningful parallel between the efficacy of immunotherapy and the extent of T cell dysfunction will shed light on areas where we can improve immune function to battle cancer