On the existence of nonoscillatory phase functions for second order differential equations in the high-frequency regime

We observe that solutions of a large class of highly oscillatory second order linear ordinary differential equations can be approximated using nonoscillatory phase functions. In addition, we describe numerical experiments which illustrate important implications of this fact. For example, that many special functions of great interest --- such as the Bessel functions $J_\nu$ and $Y_\nu$ --- can be evaluated accurately using a number of operations which is $O(1)$ in the order $\nu$. The present paper is devoted to the development of an analytical apparatus. Numerical aspects of this work will be reported at a later date

On the asymptotics of Bessel functions in the Fresnel regime

We introduce a version of the asymptotic expansions for Bessel functions $J_\nu(z)$, $Y_\nu(z)$ that is valid whenever $|z| > \nu$ (which is deep in the Fresnel regime), as opposed to the standard expansions that are applicable only in the Fraunhofer regime (i.e. when $|z| > \nu^2$). As expected, in the Fraunhofer regime our asymptotics reduce to the classical ones. The approach is based on the observation that Bessel's equation admits a non-oscillatory phase function, and uses classical formulas to obtain an asymptotic expansion for this function; this in turn leads to both an analytical tool and a numerical scheme for the efficient evaluation of $J_\nu(z)$, $Y_\nu(z)$, as well as various related quantities. The effectiveness of the technique is demonstrated via several numerical examples. We also observe that the procedure admits far-reaching generalizations to wide classes of second order differential equations, to be reported at a later date

Music Interventions for Chinese Patient with Parkinson\u27s Disease: Alleviating Symptoms through Arts-based Interventions

Care for the elderly is increasingly important, especially in long-term care centers. How to maintain the quality of life of the elderly is a very important issue for a therapist. There are many therapists dedicated to developing unique expressive arts therapy treatments for residents in long-term care centers. For these customized treatments, therapists need to consider a number of factors, including the problems for referral, medications, and diagnosis. In addition, the patient\u27s cultural background is one of the factors that must be considered in designing a treatment plan. This inquiry explores how music therapy interventions can help a patient from Eastern culture with Parkinson\u27s disease in long term care system. This treatment plan will focus on alleviating Parkinson’s disease symptoms through arts-based interventions, helping the patient adapt to the new living environment, reducing their depression and self-isolation. Because the patient is from Eastern culture, the design of this intervention will be based on Peking drama and traditional Chinese arts. The design uses the familiar art form of the patient to help the patient adapt to the new living environment. In addition, the therapist spoke Chinese in the sessions. The results showed that the patient gradually adapted to this new long-term care facility

Quench Dynamics of Topological Maximally-Entangled States

We investigate the quench dynamics of the one-particle entanglement spectra (OPES) for systems with topologically nontrivial phases. By using dimerized chains as an example, it is demonstrated that the evolution of OPES for the quenched bi-partite systems is governed by an effective Hamiltonian which is characterized by a pseudo spin in a time-dependent pseudo magnetic field $\vec{S}(k,t)$. The existence and evolution of the topological maximally-entangled edge states are determined by the winding number of $\vec{S}(k,t)$ in the $k$-space. In particular, the maximally-entangled edge states survive only if nontrivial Berry phases are induced by the winding of $\vec{S}(k,t)$. In the infinite time limit the equilibrium OPES can be determined by an effective time-independent pseudo magnetic field \vec{S}_{\mb{eff}}(k). Furthermore, when maximally-entangled edge states are unstable, they are destroyed by quasiparticles within a characteristic timescale in proportional to the system size.Comment: 5 pages, 3 figure

Edge State, Entanglement Entropy Spectra and Critical Hopping Coupling of Anisotropic Honeycomb Lattice

For a bipartite honeycomb lattice, we show that the Berry phase depends not only on the shape of the system but also on the hopping couplings. Using the entanglement entropy spectra obtained by diagonalizing the block Green's function matrices, the maximal entangled state with the eigenvalue $\lambda_m=1/2$ of the reduced density matrix is shown to have one-to-one correspondence to the zero energy states of the lattice with open boundaries, which depends on the Berry phase. For the systems with finite bearded edges along $x$-direction we find critical hopping couplings: the maximal entangled states (zero-energy states) appear pair by pair if one increases the hopping coupling $h$ over the critical couplings $h_c$s.Comment: 4 pages, 4 figure

Malware Image Classification using Machine Learning with Local Binary Pattern

Malware classification is a critical part in the cybersecurity. Traditional methodologies for the malware classification typically use static analysis and dynamic analysis to identify malware. In this paper, a malware classification methodology based on its binary image and extracting local binary pattern (LBP) features are proposed. First, malware images are reorganized into 3 by 3 grids which is mainly used to extract LBP feature. Second, the LBP is implemented on the malware images to extract features in that it is useful in pattern or texture classification. Finally, Tensorflow, a library for machine learning, is applied to classify malware images with the LBP feature. Performance comparison results among different classifiers with different image descriptors such as GIST, a spatial envelope, and the LBP demonstrate that our proposed approach outperforms others

Living Below the Line: Racial and Ethnic Disparities in Economic Security among Older Americans, 2022

New estimates based on the 2022 Elder IndexTM show that the risk of economic insecurity in later life is especially high for people of color. Comparing household incomes to the Elder Index, we calculate the percentage of independent older adults with incomes that fall short of what is required to support economic security. National averages suggest that among older people living alone, 43% who are White, 59% of those who are Asian, 61% of those who are Black, and 67% of those who are Latino have annual incomes below the Elder Index. The risk of economic insecurity is lower among couples than among singles but is still substantially higher for people of color. Economic insecurity is especially prevalent among single women of color. Our estimates suggest that 12 million U.S. adults aged 65 or older in one- and two-person households struggle to make ends meet, facing financial challenges in their efforts to age in place and in community

Living Below the Line: Economic Insecurity and Older Americans, Insecurity in Massachusetts, 2022

New estimates from the 2022 Elder IndexTM reveal that the cost of living in Massachusetts has increased substantially in recent years for older adults, especially for renters. The Elder Index measures the necessary costs faced by households made up of one or two older adults, calculated county by county for the entire United States. Estimated costs are higher in Massachusetts than in any other state in the nation. Within the Commonwealth, the Elder Index is lowest in Western Massachusetts, and highest in Metro Boston, Martha’s Vineyard and Nantucket, with differences in the Elder Index across locations accounted for largely by the cost of housing. Comparing household incomes to the Elder Index, we calculate the percentage of independent older adults with incomes that do not support economic security. Massachusetts ranks at the top among the states in percentage of older singles with incomes below the Elder Index value, at 57%, and it ranks fourth nationally among couples, at 26%. Together, these figures suggest that nearly 300,000 Massachusetts single or coupled residents aged 65 or older live with incomes below what it takes to cover essentials

Living Below the Line: Economic Insecurity and Older Americans, Insecurity in the States, 2022

New estimates from the 2022 Elder IndexTM suggest that nearly half of older adults living alone, and one out of five older couples, lack the financial resources required to pay for basic needs. We compared household incomes for adults age 65 and above living in one- and two-person households to the 2022 Elder Index for each state to calculate Economic Insecurity Rates (EIRs), the percentage of independent adults age 65 or older with annual incomes that do not support economic security. The EIRs allow a better understanding of how many and which older adults are experiencing economic insecurity. National averages suggest that 48% of older adults living alone and 21% of older couples have annual incomes below the Elder Index value. In every state, more than one-third of older singles are at risk of being unable to afford basic needs and age in their own homes

Late-Life Gender Disparities in Economic Security: Evidence from the 2022 Elder Index

Estimates from the 2022 Elder Index illustrate the elevated risk of economic insecurity experienced by older women, especially those living alone. We use the Elder Index to calculate the percentage of older adults living in one- and two-person households with annual incomes that do not support economic security. National averages suggest that half of older women living alone, along with 42% of older men living alone, have annual incomes below the Elder Index. In addition, 21% of older couples have annual incomes below the Elder Index. Women in same-sex couples experience greater levels of disadvantage than men in same-sex couples and people in opposite sex couples. Moreover, women who are age 85 or older are at especially high risk of economic insecurity. These findings highlight the sizable impact of gender inequality throughout the life course on retirement security