Parameter estimation in pair hidden Markov models

This paper deals with parameter estimation in pair hidden Markov models (pair-HMMs). We first provide a rigorous formalism for these models and discuss possible definitions of likelihoods. The model being biologically motivated, some restrictions with respect to the full parameter space naturally occur. Existence of two different Information divergence rates is established and divergence property (namely positivity at values different from the true one) is shown under additional assumptions. This yields consistency for the parameter in parametrization schemes for which the divergence property holds. Simulations illustrate different cases which are not covered by our results.Comment: corrected typo

Quantum hypothesis testing with group symmetry

The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound and Stein's lemma, and derive bounds on these quantities in terms of their corresponding statistical distance measures. A special emphasis is put on the comparison of the performances of group-invariant and unrestricted measurements.Comment: 33 page

Advances and challenges in geroscience research: An update

Aging remains the most pervasive risk factor for a wide range of chronic diseases that afflict modern societies. In the United States alone, incidence of age-related diseases (e.g., cardiovascular disease, stroke, Alzheimer’s disease, vascular cognitive impairment and dementia, cancer, hypertension, type-2 diabetes, chronic obstructive pulmonary disease, and osteoarthritis) is on the rise, posing an unsustainable socioeconomic burden even for the most developed countries. Tackling each and every age-related disease alone is proving to be costly and ineffective. The emerging field of geroscience has posed itself as an interdisciplinary approach that aims to understand the relationship between the biology of aging and the pathophysiology of chronic age-related diseases. According to the geroscience concept, aging is the single major risk factor that underlies several age-related chronic diseases, and manipulation of cellular and systemic aging processes can delay the manifestation and/or severity of these age-related chronic pathologies. The goal of this endeavor is to achieve health improvements by preventing/delaying the pathogenesis of several age-related diseases simultaneously in the elderly population by targeting key cellular and molecular processes of aging instead of managing diseases of aging as they arise individually. In this review, we discuss recent advances in the field of geroscience, highlighting their implications for potential future therapeutic targets and the associated scientific challenges and opportunities that lay ahead

Security of Quantum Key Distribution with entangled quNits

We consider a generalisation of Ekert's entanglement-based quantum cryptographic protocol where qubits are replaced by qu$N$its (i.e., N-dimensional systems). In order to study its robustness against optimal incoherent attacks, we derive the information gained by a potential eavesdropper during a cloning-based individual attack. In doing so, we generalize Cerf's formalism for cloning machines and establish the form of the most general cloning machine that respects all the symmetries of the problem. We obtain an upper bound on the error rate that guarantees the confidentiality of quNit generalisations of the Ekert's protocol for qubits.Comment: 15 pages, equation 15 and conclusions corrected the 14th of April 2003, new results adde

Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics

A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging differential-functional equation yields a two-parameter class of generalized logarithms, from which entropies and power-law distributions follow: these distributions could be relevant in many anomalous systems. Within the specified range of parameters, these entropies possess positivity, continuity, symmetry, expansibility, decisivity, maximality, concavity, and are Lesche stable. The Boltzmann-Shannon entropy and some one parameter generalized entropies already known belong to this class. These entropies and their distribution functions are compared, and the corresponding deformed algebras are discussed.Comment: Version to appear in PRE: about 20% shorter, references updated, 13 PRE pages, 3 figure