Non-Lipschitz points and the SBV regularity of the minimum time function

This paper is devoted to the study of the Hausdorff dimension of the singular set of the minimum time function $T$ under controllability conditions which do not imply the Lipschitz continuity of $T$. We consider first the case of normal linear control systems with constant coefficients in $\mathbb{R}^N$. We characterize points around which $T$ is not Lipschitz as those which can be reached from the origin by an optimal trajectory (of the reversed dynamics) with vanishing minimized Hamiltonian. Linearity permits an explicit representation of such set, that we call $\mathcal{S}$. Furthermore, we show that $\mathcal{S}$ is $\mathcal{H}^{N-1}$-rectifiable with positive $\mathcal{H}^{N-1}$-measure. Second, we consider a class of control-affine \textit{planar} nonlinear systems satisfying a second order controllability condition: we characterize the set $\mathcal{S}$ in a neighborhood of the origin in a similar way and prove the $\mathcal{H}^1$-rectifiability of $\mathcal{S}$ and that $\mathcal{H}^1(\mathcal{S})>0$. In both cases, $T$ is known to have epigraph with positive reach, hence to be a locally $BV$ function (see \cite{CMW,GK}). Since the Cantor part of $DT$ must be concentrated in $\mathcal{S}$, our analysis yields that $T$ is $SBV$, i.e., the Cantor part of $DT$ vanishes. Our results imply also that $T$ is locally of class $\mathcal{C}^{1,1}$ outside a $\mathcal{H}^{N-1}$-rectifiable set. With small changes, our results are valid also in the case of multiple control input.Comment: 23 page

Streaming Potential and Electro-osmosis Measurements to Characterize Porous Materials

Characterizing the streaming potential and electroosmosis properties of porous media is essential in applying seismoelectric and electroseismic phenomena for oil exploration. Some parameters such as porosity, permeability, formation factor, pore size, the number of pores, and the zeta potential of the samples can be obtained from elementary measurements. We performed streaming potential and electro-osmosis measurements for 6 unconsolidated samples made of spherical polymer particles. To check the validity of the measurements, we also used alternative analysis to determine the average pore size of the samples and, moreover, used a sample made of sand particles to determine the zeta potential

Mere Exposure Effects: Presence of parasitic mites induce a change in the metabolic rate of flies independent of infection

Parasites affect host physiology and populations in numerous ways including: increased mortality, decreased fecundity, and changes to host behavior. Many documented effects depend on infection to explain changes, for example: parasite blood feeding, tissue damage, and costs of immune responses. However, the effects that the mere presence of parasites have on their hosts is relatively unexplored. We study a fruit fly - mite model system. Macrocheles Domesticae is an ectoparasite that reversibly attaches to Drosophila Hydei as a means of transportation as well as feeding on host hemolymph. Since flies must move between resource patches, the effects of parasite infection on flight are significant. This system is can be used to illustrate host-parasite dynamics. We take an ecological physiology perspective and link physical changes in organisms to the larger scale processes of ecology; we deploy respirometry to compare energy consumption of flies under various conditions. Carbon Dioxide produced is measured as a flow, and linked to energy consumption by the cellular respiration equation. We hypothesize that host flight will be impaired by infection. Bioenergetic costs of infection imply this effect will be present even if mites are removed prior to flight. Results show that both flies carrying mites, and flies infected prior to flight, both hover for reduced lengths of time. Additionally, both actively resisting mites, as well as mere exposure to them, increases the Carbon Dioxide output of the host. These results have implications for host fitness and energy budgets in both the evolution and ecology of host-parasite interactions. *Indicates faculty mento

Multipole Expansion for the Electron-Nucleus Scattering at High Energies in the Unified Electroweak Theory

The article presents the multipole expansion for the electron-nucleus scattering cross section at high energies within the framework of the unified electroweak theory. The electroweak currents of the nucleus are expanded into simple components with definite angular momentum, which are called the multipole form factors. The multipole expansion of the cross section is a consequence of the above expansion. Besides the familiar electromagnetic form factors, there are weak form factors related to weak interactions, corresponding to the vector and axial (pseudovector) weak currents. We do not use the impulse approximation, the multipole form factors are calculated directly, using only the Born approximation. We will present some examples in the next paper.Comment: 7 pages, 0 figur

Microbial ecology of Thiobacillus ferrooxidans

FINAL TECHNICAL REPORT TO U.S. DEPARTMENT OF THE INTERIOR Geological Survey Washington. D.C.The contents of this report were developed in part under a grant from the Department of the Interior, U.S. Geological Survey. Grant number 14-08-0001-61313

New records for the liverwort and hornwort flora of Vietnam, 1

After the examination of the Cryptogam collection in the Herbarium of the University of Science, Vietnam National University Ho Chi Minh City (PHH), 25 species proved to be new to Vietnam, including one hornwort and 24 liverworts. Among them, four genera: Denotarisia Grolle, Gongylanthus Nees, Leiomitra Lindb. and Lepicolea Dumort. are new records for the country. Diagnostic characters and illustrations are given for some taxa, as well as locality notes and habitat descriptions are provided for each collecting area

Loss of histone macroH2A1 in hepatocellular carcinoma cells promotes paracrine-mediated chemoresistance and CD4+CD25+FoxP3+ regulatory T cells activation

Rationale: Loss of histone macroH2A1 induces appearance of cancer stem cells (CSCs)-like cells in hepatocellular carcinoma (HCC). How CSCs interact with the tumor microenvironment and the adaptive immune system is unclear. Methods: We screened aggressive human HCC for macroH2A1 and CD44 CSC marker expression. We also knocked down (KD) macroH2A1 in HCC cells, and performed integrated transcriptomic and secretomic analyses. Results: Human HCC showed low macroH2A1 and high CD44 expression compared to control tissues. MacroH2A1 KD CSC-like cells transferred paracrinally their chemoresistant properties to parental HCC cells. MacroH2A1 KD conditioned media transcriptionally reprogrammed parental HCC cells activated regulatory CD4+/CD25+/FoxP3+ T cells (Tregs). Conclusions: Loss of macroH2A1 in HCC cells drives cancer stem-cell propagation and evasion from immune surveillance