Quantum Hopfield neural network

Quantum computing allows for the potential of significant advancements in both the speed and the capacity of widely used machine learning techniques. Here we employ quantum algorithms for the Hopfield network, which can be used for pattern recognition, reconstruction, and optimization as a realization of a content-addressable memory system. We show that an exponentially large network can be stored in a polynomial number of quantum bits by encoding the network into the amplitudes of quantum states. By introducing a classical technique for operating the Hopfield network, we can leverage quantum algorithms to obtain a quantum computational complexity that is logarithmic in the dimension of the data. We also present an application of our method as a genetic sequence recognizer.Comment: 13 pages, 3 figures, final versio

Concepts in ichnotaxonomy illustrated by small round holes in shells

La clasificación de las pistas fósiles requiere un doble sistema de nomenclatura. El nombre de la pista fósil (ichnotaxon) está basado en la morfologia de la estructura, mientras que el taxon biológico  representa la posicion filogenética que se interpreta del organismo causante. Los dos sistemas de nomenclatura no se pueden intercambiar, y ambos son necesarios para la completa clasificacion dela pista. A muchas de estas pistas no les ha sido aún atribuido unichnotaxon descriptivo, pero ya que las  pistas fósiles re quieren nombres si han de ser tratadas sistemáticamente, se ofrece comunmente en tales  casos un biotaxon interpretativo en lugar del ichnotaxon que no se ha descritotodavia Este procedimiento tiende a desviar la atención de la verdadera naturaleza de la pista fósil e implica una falsa  exactitud en la determinación filogenética, lo cual conduce a conclusiones paleobiologicas poco seguras. Estos puntos quedan bien ilustrados por el ejemplo de unas perforaciones pequeíias y redondas sobre  conchas. Son pistas fósiles abundantes y, no teniendo ichnotaxon, tienden a ser relacionadas con la  accion perforante de los gasteropedos-naticidos y muricidos-sobre conchas. Sin embargo, varios grupos  más de gasteropodos producen perforaciones redondas, al igual que los cefalopodos octopodos,  turbelarios, nemátodos y braquiópodos articulados, pero su acción es poco conocida. Antes de embarcarse en tales especulaciones, como son los organismos causantes, es necesario un ichnotaxón para atraer la atención hacia estas pistas fosiles y aumentarel rigorde su tratamiento. Sólo cuando sumorfologia y distribución sean mejor conocidas estaremos en una posición mejor para discutir sus  atribuciones filogenéticas

Unifying approach to the quantification of bipartite correlations by Bures distance

The notion of distance defined on the set of states of a composite quantum system can be used to quantify total, quantum and classical correlations in a unifying way. We provide new closed formulae for classical and total correlations of two-qubit Bell-diagonal states by considering the Bures distance. Complementing the known corresponding expressions for entanglement and more general quantum correlations, we thus complete the quantitative hierarchy of Bures correlations for Bell-diagonal states. We then explicitly calculate Bures correlations for two relevant families of states: Werner states and rank-2 Bell-diagonal states, highlighting the subadditivity which holds for total correlations with respect to the sum of classical and quantum ones when using Bures distance. Finally, we analyse a dynamical model of two independent qubits locally exposed to non-dissipative decoherence channels, where both quantum and classical correlations measured by Bures distance exhibit freezing phenomena, in analogy with other known quantifiers of correlations.Comment: 18 pages, 4 figures; published versio

Person-centered learning in a collegiate jazz combo

Incorporating person-centered approaches in educational settings can help students become more actively engaged in learning processes. Subsequently, the students may experience whole-person learning through cognitive, emotional, and experiential means, develop greater self-discipline, and emerge as more fully-functioning persons. When a classroom becomes a person-centered learning community, the entire person grows holistically instead of merely acquiring information. The learning is also more personally meaningful and pervasive, in that, by the students’ own accounts the growth that they achieve is beneficial to them in their broader lives. In this qualitative case study, I used Carl Rogers and Jerome Freiberg’s (1994) person-centered learning theory as a lens to explore a collegiate jazz combo. The combo was located at a university in the Western United States. The purpose of this study was to discover how the combo functioned as a person-centered learning community; and to explore the learning and development that occurred in the combo, which related to experiencing whole-person learning, building self-discipline, and emerging as more fully-functioning persons. Over the course of one semester of instruction, I gathered data through observations and interviews as I participated in the combo as the faculty coach. I recorded my observations in fieldnotes and transcribed the audio-recorded interviews. I analyzed and coded the data; and then grouped the coded data into categorical themes. The findings I present are based on the themes that emerged. In this study, I found that the combo functioned as a person-centered learning community because the members actively engaged in the combo all throughout the semester. The members composed, arranged, and improvised music regularly. They worked together cooperatively to prepare and play tunes, and to improve as an ensemble. I facilitated and coached (rather than directed and controlled) the members’ music making and learning in the ensemble. In the combo, the members and I communicated verbally with each other as we socialized and worked on improving the music; and the members communicated nonverbally and musically as they played and performed their music. The environment created by the members and myself was positive, supportive, and fun. Because the combo functioned as a person-centered learning community, the members grew holistically. The members became more self-disciplined as musicians and persons. They developed greater communication and social skills, improved at time management, gained more control over their individual actions and ability to play music, learned to make better choices, and matured in their leadership. The members also experienced whole-person learning in the combo. They learned through cognitive means, and grew in their cognitive function. They grew emotionally and gained greater understanding through emotional and feeling driven processes. Furthermore, the members grew experientially and became more capable of acting and performing well in a variety of given scenarios and situations. The members’ learning was personally relevant and meaningful because they were able to make progress on their own goals as musicians and persons; and because their education in the combo prepared them for greater success as human beings and musicians outside the classroom. By engaging in learning processes that involved all three aspects of whole-person learning—cognition, emotions, and experience—the members became more fully-functioning musicians and persons throughout the semester. Based upon my findings, I recommend that educators implement principles of person-centered learning into their classrooms and programs. Teachers and administrators should design classes and overall programs so that they provide students with sufficient opportunities to grow as whole-persons, gain greater self-discipline, and emerge as more fully-functioning persons. Students need chances to self-discover information and processes, to utilize gained knowledge, skills, and understanding to make their own creations, and to cooperatively work with their teachers and/or peers in self-directed situations. In music education settings, there needs to be a greater balance between large ensemble opportunities versus small-group settings where students compose, improvise, and arrange music themselves. Adjusting individual classes and overall programs so that they are more person-centered may help students leave the classroom more prepared to continue learning and developing as persons outside the classroom. The students may likewise leave the classroom more capable of successfully functioning and contributing in an ever-changing world