An instability of higher-dimensional rotating black holes

We present the first example of a linearized gravitational instability of an asymptotically flat vacuum black hole. We study perturbations of a Myers-Perry black hole with equal angular momenta in an odd number of dimensions. We find no evidence of any instability in five or seven dimensions, but in nine dimensions, for sufficiently rapid rotation, we find perturbations that grow exponentially in time. The onset of instability is associated with the appearance of time-independent perturbations which generically break all but one of the rotational symmetries. This is interpreted as evidence for the existence of a new 70-parameter family of black hole solutions with only a single rotational symmetry. We also present results for the Gregory-Laflamme instability of rotating black strings, demonstrating that rotation makes black strings more unstable.Comment: 38 pages, 13 figure

Extracellular electrical signals in a neuron-surface junction: model of heterogeneous membrane conductivity

Signals recorded from neurons with extracellular planar sensors have a wide range of waveforms and amplitudes. This variety is a result of different physical conditions affecting the ion currents through a cellular membrane. The transmembrane currents are often considered by macroscopic membrane models as essentially a homogeneous process. However, this assumption is doubtful, since ions move through ion channels, which are scattered within the membrane. Accounting for this fact, the present work proposes a theoretical model of heterogeneous membrane conductivity. The model is based on the hypothesis that both potential and charge are distributed inhomogeneously on the membrane surface, concentrated near channel pores, as the direct consequence of the inhomogeneous transmembrane current. A system of continuity equations having non-stationary and quasi-stationary forms expresses this fact mathematically. The present work performs mathematical analysis of the proposed equations, following by the synthesis of the equivalent electric element of a heterogeneous membrane current. This element is further used to construct a model of the cell-surface electric junction in a form of the equivalent electrical circuit. After that a study of how the heterogeneous membrane conductivity affects parameters of the extracellular electrical signal is performed. As the result it was found that variation of the passive characteristics of the cell-surface junction, conductivity of the cleft and the cleft height, could lead to different shapes of the extracellular signals

Refined topological amplitudes in N=1 flux compactification

We study the implication of refined topological string amplitudes in the supersymmetric N=1 flux compactification. They generate higher derivative couplings among the vector multiplets and graviphoton with generically non-holomorphic moduli dependence. For a particular term, we can compute them by assuming the geometric engineering. We claim that the Dijkgraaf-Vafa large N matrix model with the beta-ensemble measure directly computes the higher derivative corrections to the supersymmetric effective action of the supersymmetric N=1$ gauge theory.Comment: 16 pages, v2: reference adde

Searching for plasticity in dissociated cortical cultures on multi-electrode arrays

We attempted to induce functional plasticity in dense cultures of cortical cells using stimulation through extracellular electrodes embedded in the culture dish substrate (multi-electrode arrays, or MEAs). We looked for plasticity expressed in changes in spontaneous burst patterns, and in array-wide response patterns to electrical stimuli, following several induction protocols related to those used in the literature, as well as some novel ones. Experiments were performed with spontaneous culture-wide bursting suppressed by either distributed electrical stimulation or by elevated extracellular magnesium concentrations as well as with spontaneous bursting untreated. Changes concomitant with induction were no larger in magnitude than changes that occurred spontaneously, except in one novel protocol in which spontaneous bursts were quieted using distributed electrical stimulation

Refined Cigar and Omega-deformed Conifold

Antoniadis et al proposed a relation between the Omega-deformation and refined correlation functions of the topological string theory. We investigate the proposal for the deformed conifold geometry from a non-compact Gepner model approach. The topological string theory on the deformed conifold has a dual description in terms of the c=1 non-critical string theory at the self-dual radius, and the Omega-deformation yields the radius deformation. We show that the refined correlation functions computed from the twisted SL(2,R)/U(1) Kazama-Suzuki coset model at level k=1 have direct c=1 non-critical string theory interpretations. After subtracting the leading singularity to procure the 1PI effective action, we obtain the agreement with the proposal.Comment: 15 pages, v2: reference added, v3: published versio

The Nuts and Bolts of Einstein-Maxwell Solutions

We find new non-supersymmetric solutions of five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are regular, horizonless and have the same asymptotic charges as non-extremal charged black holes. An essential ingredient in our construction is a four-dimensional Euclidean base which is a solution to Einstein-Maxwell equations. We construct stationary solutions based on the Euclidean dyonic Reissner-Nordstrom black hole as well as a six-parameter family with a dyonic Kerr-Newman-NUT base. These solutions can be viewed as compactifications of eleven-dimensional supergravity on a six-torus and we discuss their brane interpretation.Comment: 29 pages, 3 figure

Holographic Penta and Hepta Quark State in Confining Gauge Theories

We study a new embedding solutions of D5 brane in an asymptotic AdS${}_5\times S^5$ space-time, which is dual to a confining $SU(N_c)$ gauge theory. The D5 brane is wrapped on $S^5$ as in the case of the vertex of holographic baryon. However, the solution given here is different from the usual baryon vertex in the point that it couples to $k$-anti-quarks and $N_c+k$ quarks on the opposite two points of $S^5$, the north and south poles, respectively. The total quark number of this state is preserved as $N_c$ when minus one is assigned to anti-quark, then it forms a color singlet like the baryon. However, this includes anti-quarks and quarks, whose number is larger than that of the baryon. When we set as $N_c=3$, we find the so called penta and hepta-quark states. We study the dynamical properties of these states by solving the vertex and string configurations for such states. The mass spectra of these states and the tension of the stretched vertex are estimated, and they are compared with that of the baryon.Comment: 24 pages, 6 figure