The Grow-Shrink strategy for learning Markov network structures constrained by context-specific independences

Markov networks are models for compactly representing complex probability distributions. They are composed by a structure and a set of numerical weights. The structure qualitatively describes independences in the distribution, which can be exploited to factorize the distribution into a set of compact functions. A key application for learning structures from data is to automatically discover knowledge. In practice, structure learning algorithms focused on "knowledge discovery" present a limitation: they use a coarse-grained representation of the structure. As a result, this representation cannot describe context-specific independences. Very recently, an algorithm called CSPC was designed to overcome this limitation, but it has a high computational complexity. This work tries to mitigate this downside presenting CSGS, an algorithm that uses the Grow-Shrink strategy for reducing unnecessary computations. On an empirical evaluation, the structures learned by CSGS achieve competitive accuracies and lower computational complexity with respect to those obtained by CSPC.Comment: 12 pages, and 8 figures. This works was presented in IBERAMIA 201

Critical States Embedded in the Continuum

We introduce a class of critical states which are embedded in the continuum (CSC) of one-dimensional optical waveguide array with one non-Hermitian defect. These states are at the verge of being fractal and have real propagation constant. They emerge at a phase transition which is driven by the imaginary refractive index of the defect waveguide and it is accompanied by a mode segregation which reveals analogies with the Dicke super -radiance. Below this point the states are extended while above they evolve to exponentially localized modes. An addition of a background gain or loss can turn these localized states to bound states in the continuum.Comment: 4.5 pages, 3 figures, 1 page of supplementary material including one figur

Response of discrete nonlinear systems with many degrees of freedom

We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscillations. The amplitude equation that we derive here from first principles exhibits a wavenumber dependent bifurcation similar in character to the behavior known to exist in fluids undergoing the Faraday wave instability. We confirm this behavior numerically and make suggestions for testing it experimentally with MEMS and NEMS resonators.Comment: Version 2 is an expanded version of the article, containing detailed steps of the derivation that were left out in version 1, but no additional result

Tax Treatment of a Marijuana Business

Currently, twenty-eight states and the District of Columbia allow the use of marijuana for medical purposes and permit the conduct of a business marketing of marijuana for that purpose. Eight of those states and the District of Columbia permit the recreational use of marijuana. There is reason to believe that more states will decriminalize the marketing of marijuana. However, marijuana is listed in Schedule 1 of the federal Controlled Substances Act of 1970 (CSA) which makes it illegal under federal law to manufacture or distribute marijuana even when it is legal to do so under local state law. In a series of memoranda promulgated by the Justice Department in the period from 2009 to 2014, the Department announced that it would not enforce the CSA prohibition against marijuana if certain requirements are met. Consequently, even the federal government has evidenced some ambivalence as to whether the conduct of a marijuana business for medical use should be illegal

Provisions Denying a Deduction for Illegal Expenses and Expenses of an Illegal Business Should be Repealed

The federal income tax law denies a deduction for illegal expenses, for any expense (legal or otherwise) of an illegal business that is trafficking in controlled substances, for losses incurred in an unlawful activity, and for bribes, kickbacks, and rebates connected with the Medicare or Medicaid program. In this Article, the authors first describe the current treatment of those items by the tax law. The Article next explains that the current treatment constitutes a penalty for the taxpayer whose deduction is denied, and then explores why such a penalty is bad policy and conflicts with the traditional purposes and goals of punishing wrongful behavior. The principal objection to the penalty imposed by the tax law’s denial of deductions for business and profit-oriented expenses is that the manner in which the size of the tax law’s penalty is determined is completely arbitrary and bears no relationship to the seriousness of the crime or the conditions under which it was committed. Another objection to the penalty is that it would be litigated in a civil tax suit in which the taxpayer would lack the protections and rights accorded to criminal defendants even though it constitutes a punishment for criminal behavior. The penalty is especially harsh as applied to the legal expenses of a marijuana business under a more stringent Code provision given the decriminalization of marijuana by many states. The Article also contends that the denial of a deduction for unlawful medical expenses conflicts with the principle allowing the patient a deduction for whatever treatment the patient chooses so long as it is based on a bona fide effort to deal with the illness. The authors recommend that Congress act to eliminate all of these tax penalties