Bifurcations from families of periodic solutions in piecewise differential systems

Consider a differential system of the form $$x'=F_0(t,x)+\sum_{i=1}^k \varepsilon^i F_i(t,x)+\varepsilon^{k+1} R(t,x,\varepsilon),$$ where $F_i:\mathbb{S}^1 \times D \to \mathbb{R}^m$ and $R:\mathbb{S}^1 \times D \times (-\varepsilon_0,\varepsilon_0) \to \mathbb{R}^m$ are piecewise $C^{k+1}$ functions and $T$-periodic in the variable $t$. Assuming that the unperturbed system $x'=F_0(t,x)$ has a $d$-dimensional submanifold of periodic solutions with $d<m$, we use the Lyapunov-Schmidt reduction and the averaging theory to study the existence of isolated $T$-periodic solutions of the above differential system

Audible Axions

Conventional approaches to probing axions and axion-like particles (ALPs) typically rely on a coupling to photons. However, if this coupling is extremely weak, ALPs become invisible and are effectively decoupled from the Standard Model. Here we show that such invisible axions, which are viable candidates for dark matter, can produce a stochastic gravitational wave background in the early universe. This signal is generated in models where the invisible axion couples to a dark gauge boson that experiences a tachyonic instability when the axion begins to oscillate. Incidentally, the same mechanism also widens the viable parameter space for axion dark matter. Quantum fluctuations amplified by the exponentially growing gauge boson modes source chiral gravitational waves. For axion decay constants $f \gtrsim 10^{17}$ GeV, this signal is detectable by either pulsar timing arrays or space/ground-based gravitational wave detectors for a broad range of axion masses, thus providing a new window to probe invisible axion models.Comment: 8 pages, 4 figures. References added, version submitted to JHE

An analysis of a regular black hole interior model

We analyze the thermodynamical properties of the regular static and spherically symmetric black hole interior model presented by Mboyne and Kazanas. Equations for the thermodynamical quantities valid for an arbitrary density profile are deduced, and from them we show that the model is thermodynamically unstable. Evidence is also presented pointing to its dynamical instability. The gravitational entropy of this solution based on the Weyl curvature conjecture is calculated, following the recipe given by Rudjord, Gr$\varnothing$n and Sigbj$\varnothing$rn, and it is shown to have the expected behavior.Comment: 22 pages, 17 figures, accepted for publication in International Journal of Theoretical Physic

Optimal Time-dependent Sequenced Route Queries in Road Networks

In this paper we present an algorithm for optimal processing of time-dependent sequenced route queries in road networks, i.e., given a road network where the travel time over an edge is time-dependent and a given ordered list of categories of interest, we find the fastest route between an origin and destination that passes through a sequence of points of interest belonging to each of the specified categories of interest. For instance, considering a city road network at a given departure time, one can find the fastest route between one's work and his/her home, passing through a bank, a supermarket and a restaurant, in this order. The main contribution of our work is the consideration of the time dependency of the network, a realistic characteristic of urban road networks, which has not been considered previously when addressing the optimal sequenced route query. Our approach uses the A* search paradigm that is equipped with an admissible heuristic function, thus guaranteed to yield the optimal solution, along with a pruning scheme for further reducing the search space. In order to compare our proposal we extended a previously proposed solution aimed at non-time dependent sequenced route queries, enabling it to deal with the time-dependency. Our experiments using real and synthetic data sets have shown our proposed solution to be up to two orders of magnitude faster than the temporally extended previous solution.Comment: 10 pages, 12 figures To be published as a short paper in the 23rd ACM SIGSPATIA

The Development of Colombian Bond Market.

Abstract: In this paper we explore the determinants and the consequences of the development of the corporate bond market in Colombia. We use a large firm-level dataset for the period 1997-2004 and find that the larger, more profitable and more leveraged firms have a higher probability to issue bonds. The econometric results also show that the larger the treasury bond market, the lower the probability that a firm will issue bonds, suggesting the presenceof a crowding out effect. On the demand side, the panel estimations indicate that investors with larger portfolios tend to hold more corporate bonds. Also, from the viewpoint of investors, average bond issue size is a critical variable. Finally, we find that sectors that have more corporate bonds (as percentage of total liabilities) have greater loan quality, and this result is stronger during periods of banking crises. We conclude that bond market development can play an important countercyclical role during periods of financial stress.Resumen: En este trabajo exploramos los determinantes y las consecuencias del desarrollo del mercado de bonos corporativos en Colombia. Utilizamos una muestra amplia con información por firma para el período 1997-2004 y encontramos que las firmas más grandes, rentables y apalancadas tienen una mayor probabilidad de emitir bonos. Los resultados econométricos también muestran que un mayor tamaño del mercado de deuda pública tiene un efecto negativo sobre la probabilidad de las firmas de emitir bonos, lo cual sugiere un efecto de crowding out. Por el lado de la demanda, las estimaciones de panel indican que los inversionistas con portafolios grandes tienen mayor probabilidad de adquirir bonos. Así mismo, desde el punto de vista de los inversionistas, el tamaño promedio de la emisión es una variable crítica. Finalmente, encontramos que los sectores económicos en donde la participación de los bonos dentro del total de pasivos es mayor, tienen una mejor calidad de la cartera y enfrentan con mayor fortaleza los períodos de crisis. Concluimos que el mercado de bonos puede tener un importante papel contra cíclico en períodos de stress financiero.Mercado de bonos, mercado financiero; Bonos corporativos, Inversionistas, Colombia