Transitive state alignment for the quantum jensen-shannon kernel

Kernel methods provide a convenient way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. One problem with the most widely used kernels is that they neglect the locational information within the structures, resulting in less discrimination. Correspondence-based kernels, on the other hand, are in general more discriminating, at the cost of sacrificing positive-definiteness due to their inability to guarantee transitivity of the correspondences between multiple graphs. In this paper we generalize a recent structural kernel based on the Jensen-Shannon divergence between quantum walks over the structures by introducing a novel alignment step which rather than permuting the nodes of the structures, aligns the quantum states of their walks. This results in a novel kernel that maintains localization within the structures, but still guarantees positive definiteness. Experimental evaluation validates the effectiveness of the kernel for several structural classification tasks. © 2014 Springer-Verlag Berlin Heidelberg.

A continuous-time quantum walk kernel for unattributed graphs

Kernel methods provide a way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. In this paper, we propose a novel kernel on unattributed graphs where the structure is characterized through the evolution of a continuous-time quantum walk. More precisely, given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic. With this new graph to hand, we compute the density operators of the quantum systems representing the evolutions of two suitably defined quantum walks. Finally, we define the kernel between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Analysis of nocturnal oxygen saturation recordings using kernel entropy to assist in sleep apnea-hypopnea diagnosis

In this study, a new entropy measure known as kernel entropy (KerEnt), which quantifies the irregularity in a series, was applied to nocturnal oxygen saturation (SaO 2) recordings. A total of 96 subjects suspected of suffering from sleep apnea-hypopnea syndrome (SAHS) took part in the study: 32 SAHS-negative and 64 SAHS-positive subjects. Their SaO 2 signals were separately processed by means of KerEnt. Our results show that a higher degree of irregularity is associated to SAHS-positive subjects. Statistical analysis revealed significant differences between the KerEnt values of SAHS-negative and SAHS-positive groups. The diagnostic utility of this parameter was studied by means of receiver operating characteristic (ROC) analysis. A classification accuracy of 81.25% (81.25% sensitivity and 81.25% specificity) was achieved. Repeated apneas during sleep increase irregularity in SaO 2 data. This effect can be measured by KerEnt in order to detect SAHS. This non-linear measure can provide useful information for the development of alternative diagnostic techniques in order to reduce the demand for conventional polysomnography (PSG). © 2011 IEEE.

HIV, cardiovascular diseases, and chronic arsenic exposure co-exist in a positive synergy

Recent epidemiological evidences indicate that arsenic exposure increases risk of atherosclerosis, cardio vascular diseases (CVD) such as hypertension, atherosclerosis, coronary artery disease (CAD) and microangiopathies in addition to the serious global health concern related to its carcinogenic effects. In experiments on animals, acute and chronic exposure to arsenic directly correlates with cardiac tachyarrhythmia, and atherogenesis in a concentration and duration dependent manner. Moreover, the other effects of long-term arsenic exposure include induction of non-insulin dependent diabetes by mechanisms yet to be understood. On the other hand, there are controversial issues, gaps in knowledge, and future research priorities in accelerated incidences of CVD and mortalities in patients with HIV who are under long-termanti-retroviral therapy (ART). Although, both HIV infection itself and various components of ART initiate significant pathological alterations in the myocardium and the vasculature, simultaneous environmental exposure to arsenic which is more convincingly being recognized as a facilitator of HIV viral cycling in the infected immune cells, may contribute an additional layer of adversity in these patients. A high degree of suspicion and early screening may allow appropriate interventional guidelines to improve the quality of lives of those affected. In this mini-review which have been fortified with our own preliminary data, we will discuss some of the key current understating of chronic arsenic exposure, and its possible impact on the accelerated HIV/ART induced CVD. The review will conclude with notes on recent developments in mathematical modeling in this field that probabilistically forecast incidence prevalence as functions of aging and life style parameters, most of which vary with time themselves; this interdisciplinary approach provides a complementary kernel to conventional biology.