Novel Fiber Design for Wideband Conversion and Amplification in Multimode Fibers

We propose an operating principle to achieve broadband and highly tunable mode conversion and amplification exploiting inter-modal four wave mixing in a multimode fiber. A bandwidth of 30 nanometers is demonstrated by properly designing a simple step-index silica fiber.Comment: Ecoc conference 201

Minimizing the Repayment Cost of Federal Student Loans

Federal student loans are fixed-rate debt contracts with three main special features: (i) borrowers can use income-driven schemes to make payments proportional to their income above subsistence; (ii) after several years of being in good standing, the remaining balance is forgiven but taxed as ordinary income; and (iii) accrued interest is simple, i.e., not capitalized. For a very small loan, the cost-minimizing repayment strategy dictates maximum payments until full repayment, forgoing both income-driven schemes and forgiveness. For a very large loan, the minimal payments allowed by income-driven schemes are optimal. For intermediate balances, the optimal repayment strategy may entail an initial period of minimum payments to exploit the noncapitalization of accrued interest, but when the principal is being reimbursed maximal payments always precede minimum payments. Income-driven schemes and simple accrued interest mostly benefit borrowers with very large balances

Informational efficiency and welfare

In a continuous-time market with a safe rate and a risky asset that pays a dividend stream depending on a latent state of the economy, several agents make consumption and investment decisions based on public information–prices and dividends–and private signals. If each investor has constant absolute risk aversion, equilibrium prices do not reveal all the private signals, but lead to the same estimate of the state of the economy that one would hypothetically obtain from the knowledge of all private signals. Accurate information leads to low volatility, ostensibly improving market efficiency, but also reduces each agent’s consumption through a decrease in the price of risk. Thus, informational efficiency is reached at the expense of agents’ welfare

Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs

We show that the lack of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probability measures, together with an adapted process with values between the bid-ask spreads that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska's classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs

Observation of a Modulational Instability in Bose-Einstein condensates

We observe the breakup dynamics of an elongated cloud of condensed $^{85}$Rb atoms placed in an optical waveguide. The number of localized spatial components observed in the breakup is compared with the number of solitons predicted by a plane-wave stability analysis of the nonpolynomial nonlinear Schr\"odinger equation, an effective one-dimensional approximation of the Gross-Pitaevskii equation for cigar-shaped condensates. It is shown that the numbers predicted from the fastest growing sidebands are consistent with the experimental data, suggesting that modulational instability is the key underlying physical mechanism driving the breakup.Comment: 6 pages, 5 figure

Methyl-CpG-binding protein 2 mediates overlapping mechanisms across brain disorders

MECP2 and its product, Methyl-CpG binding protein 2 (MeCP2), are mostly known for their association to Rett Syndrome (RTT), a rare neurodevelopmental disorder. Additional evidence suggests that MECP2 may underlie other neuropsychiatric and neurological conditions, and perhaps modulate common presentations and pathophysiology across disorders. To clarify the mechanisms of these interactions, we develop a method that uses the binding properties of MeCP2 to identify its targets, and in particular, the genes recognized by MeCP2 and associated to several neurological and neuropsychiatric disorders. Analysing mechanisms and pathways modulated by these genes, we find that they are involved in three main processes: neuronal transmission, immuno-reactivity, and development. Also, while the nervous system is the most relevant in the pathophysiology of the disorders, additional systems may contribute to MeCP2 action through its target genes. We tested our results with transcriptome analysis on Mecp2-null models and cells derived from a patient with RTT, confirming that the genes identified by our procedure are directly modulated by MeCP2. Thus, MeCP2 may modulate similar mechanisms in different pathologies, suggesting that treatments for one condition may be effective for related disorders

Temporal spying and concealing process in fibre-optic data transmission systems through polarization bypass

International audienceRecent research has been focused on the ability to manipulate a light beam in such a way to hide, namely to cloak, an event over a finite time or localization in space. The main idea is to create a hole or a gap in the spatial or time domain so as to allow for an object or data to be kept hidden for a while and then to be restored. By enlarging the field of applications of this concept to telecommunications, researchers have recently reported the possibility to hide transmitted data in an optical fibre. Here we report the first experimental demonstration of perpetual temporal spying and blinding process of optical data in fibre-optic transmission line based on polarization bypass. We successfully characterize the performance of our system by alternatively copying and then concealing 100% of a 10-Gbit s-1 transmitted signal.

On the Existence of Shadow Prices

For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless "shadow market" that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper we present a counterexample which shows that shadow prices may fail to exist. On the other hand, we prove that short selling constraints are a sufficient condition to warrant their existence, even in very general multi-currency market models with possibly discontinuous bid-ask-spreads.Comment: 14 pages, 1 figure, to appear in "Finance and Stochastics

Stochastic evolution equations driven by Liouville fractional Brownian motion

Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in the interval (0,1). For Hurst parameters in (0,1/2) we show that a function F:(0,T)\to L(H,E) is stochastically integrable with respect to an H-cylindrical Liouville fBm if and only if it is stochastically integrable with respect to an H-cylindrical fBm with the same Hurst parameter. As an application we show that second-order parabolic SPDEs on bounded domains in \mathbb{R}^d, driven by space-time noise which is white in space and Liouville fractional in time with Hurst parameter in (d/4,1) admit mild solution which are H\"older continuous both and space.Comment: To appear in Czech. Math.